{"id":140284,"date":"2025-06-30T16:25:48","date_gmt":"2025-06-30T08:25:48","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=140284"},"modified":"2025-06-30T16:27:14","modified_gmt":"2025-06-30T08:27:14","slug":"lafbs132_20250521-8-en","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en","title":{"rendered":"2.1.2 Linear Dependence in Image Data"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"140284\" class=\"elementor elementor-140284\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-16700d17 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"16700d17\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1832f798\" data-id=\"1832f798\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-20 elementor-section elementor-top-section elementor-element elementor-element-6ad968e6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6ad968e6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-52987d63\" data-id=\"52987d63\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e5808cb elementor-widget elementor-widget-heading\" data-id=\"e5808cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">2.1.2 Linear Dependence in Image Data<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7aec5b11 elementor-widget elementor-widget-video\" data-id=\"7aec5b11\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/j4QiJ96wi7A&quot;,&quot;modestbranding&quot;:&quot;yes&quot;,&quot;lazy_load&quot;:&quot;yes&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;left:0;width:100%;height:100%;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-inner-section elementor-element elementor-element-7c450277 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7c450277\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"penci-ercol-100 penci-ercol-order-1 penci-sticky-ct    elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-48607404\" data-id=\"48607404\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-652aa46c elementor-widget elementor-widget-penci-button\" data-id=\"652aa46c\" data-element_type=\"widget\" data-widget_type=\"penci-button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"pcbtn-wrapper pcbtn-align-left\">\r\n\t\t\t<a class=\"pcbtn pcbtn-icon-left elementor-animation-grow\" href=\"\/?post_type=course_page&#038;p=140179\">\r\n\t\t\t\t<span class=\"pcbtn-wrapperin\">\r\n\t\t\t\t\t<span class=\"pcbtn-content\"><svg class=\"e-font-icon-svg e-fas-arrow-left\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M257.5 445.1l-22.2 22.2c-9.4 9.4-24.6 9.4-33.9 0L7 273c-9.4-9.4-9.4-24.6 0-33.9L201.4 44.7c9.4-9.4 24.6-9.4 33.9 0l22.2 22.2c9.5 9.5 9.3 25-.4 34.3L136.6 216H424c13.3 0 24 10.7 24 24v32c0 13.3-10.7 24-24 24H136.6l120.5 114.8c9.8 9.3 10 24.8.4 34.3z\"><\/path><\/svg>Back to Course Homepage<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/span>\r\n\t\t\t<\/a>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-546b36ef elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"546b36ef\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.13.3 - 28-05-2023 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider .elementor-icon{font-size:var(--divider-icon-size)}.elementor-widget-divider .elementor-divider-separator{display:flex;margin:0;direction:ltr}.elementor-widget-divider--view-line_icon .elementor-divider-separator,.elementor-widget-divider--view-line_text .elementor-divider-separator{align-items:center}.elementor-widget-divider--view-line_icon .elementor-divider-separator:after,.elementor-widget-divider--view-line_icon .elementor-divider-separator:before,.elementor-widget-divider--view-line_text .elementor-divider-separator:after,.elementor-widget-divider--view-line_text .elementor-divider-separator:before{display:block;content:\"\";border-bottom:0;flex-grow:1;border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--element-align-left .elementor-divider .elementor-divider-separator>.elementor-divider__svg:first-of-type{flex-grow:0;flex-shrink:100}.elementor-widget-divider--element-align-left .elementor-divider-separator:before{content:none}.elementor-widget-divider--element-align-left .elementor-divider__element{margin-left:0}.elementor-widget-divider--element-align-right .elementor-divider .elementor-divider-separator>.elementor-divider__svg:last-of-type{flex-grow:0;flex-shrink:100}.elementor-widget-divider--element-align-right .elementor-divider-separator:after{content:none}.elementor-widget-divider--element-align-right .elementor-divider__element{margin-right:0}.elementor-widget-divider:not(.elementor-widget-divider--view-line_text):not(.elementor-widget-divider--view-line_icon) .elementor-divider-separator{border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--separator-type-pattern{--divider-border-style:none}.elementor-widget-divider--separator-type-pattern.elementor-widget-divider--view-line .elementor-divider-separator,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:after,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:before,.elementor-widget-divider--separator-type-pattern:not([class*=elementor-widget-divider--view]) .elementor-divider-separator{width:100%;min-height:var(--divider-pattern-height);-webkit-mask-size:var(--divider-pattern-size) 100%;mask-size:var(--divider-pattern-size) 100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da19150 elementor-widget elementor-widget-shortcode\" data-id=\"da19150\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">\n<table id=\"tablepress-616\" class=\"tablepress tablepress-id-616\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH1 Fundamentals of Linear Algebra<br \/>\nCH1.1 Matrix Basics and Image Representation<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">1<\/td><td class=\"column-2\">1.1.1 Definition and Notation of Matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140181\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">2<\/td><td class=\"column-2\">1.1.2 Relationship Between Matrices and Images<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140198\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">3<\/td><td class=\"column-2\">1.1.3 Converting Images to Matrices: A Practical Implementation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140203\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH1.2 Matrix Addition and Scalar Multiplication<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">4<\/td><td class=\"column-2\">1.2.1 Matrix Addition<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140208\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">5<\/td><td class=\"column-2\">1.2.2 Applications of Matrix Addition in Image Processing<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140213\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">6<\/td><td class=\"column-2\">1.2.3 Scalar Multiplication of a Matrix<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140218\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">7<\/td><td class=\"column-2\">1.2.4 Applications of Scalar Multiplication in Image Processing<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140223\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH1.3 Matrix Multiplication<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">8<\/td><td class=\"column-2\">1.3.1 Definition of Matrix Multiplication<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140228\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">9<\/td><td class=\"column-2\">1.3.2 Matrix-Vector Multiplication<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140233\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">10<\/td><td class=\"column-2\">1.3.3 Properties of Matrix Multiplication<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140238\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">11<\/td><td class=\"column-2\">1.3.4 Identity Matrix and Zero Matrix<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140243\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH1.4 Linear Combination of Vectors<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">12<\/td><td class=\"column-2\">1.4.1 Mathematical Formulation and Operations of Linear Combination<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140248\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">13<\/td><td class=\"column-2\">1.4.2 Applications of Linear Combination in Image Processing<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140253\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">14<\/td><td class=\"column-2\">1.4.3 Vector Spaces<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140258\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\">15<\/td><td class=\"column-2\">1.4.4 Matrix Spaces<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140263\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\">16<\/td><td class=\"column-2\">1.4.5 Dimension of a Vector Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140268\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\">17<\/td><td class=\"column-2\">1.4.6 Subspaces and Their Characterization<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140273\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\">18<\/td><td class=\"column-2\">1.4.7 Subspaces in Image Processing<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140278\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH2 An Introduction to Matrix Analysis<br \/>\nCH2.1 Linear Dependence and Linear Independence<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\">19<\/td><td class=\"column-2\">2.1.1 Definition of Linear Dependence and Independence<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140283\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\">20<\/td><td class=\"column-2\">2.1.2 Linear Dependence in Image Data<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140284\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH2.2 Basis and Dimension: Describing Directionality in Image Dat<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\">21<\/td><td class=\"column-2\">2.2.1 What Is Span? Understanding Space Generation from Vectors<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140293\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\">22<\/td><td class=\"column-2\">2.2.2 Basis and Dimension<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140298\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\">23<\/td><td class=\"column-2\">2.2.3 Interpreting Dimension in Image Data<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140303\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH2.3 What Is Rank? An Intuitive Perspective<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\">24<\/td><td class=\"column-2\">2.3.1 Intuitive Meaning of Rank<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140308\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\">25<\/td><td class=\"column-2\">2.3.2 Geometric View and Implementation of Rank-One Matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140313\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-34 even\">\n\t<td class=\"column-1\">26<\/td><td class=\"column-2\">2.3.3 Outer Product of Vectors<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140318\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-35 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">CH2.4 Matrix Rank<\/td><td class=\"column-3\"><\/td>\n<\/tr>\n<tr class=\"row-36 even\">\n\t<td class=\"column-1\">27<\/td><td class=\"column-2\">2.4.1 Intuitive Meaning of Rank (Revisited)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140323\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-37 odd\">\n\t<td class=\"column-1\">28<\/td><td class=\"column-2\">2.4.2 Low-Rank Background and Sparse Foreground Model<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140328\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-38 even\">\n\t<td class=\"column-1\">29<\/td><td class=\"column-2\">2.4.3 The Significance of Low-Rank Matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140333\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-39 odd\">\n\t<td class=\"column-1\">30<\/td><td class=\"column-2\">2.4.4 Introduction to Sparse Matrix Concepts<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140338\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-40 even\">\n\t<td class=\"column-1\">31<\/td><td class=\"column-2\">Getting Started with Anaconda: Installation and Basic Usage<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=140343\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-616 from cache --><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"penci-ercol-50 penci-ercol-order-2 penci-sticky-ct    elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-5f099062\" data-id=\"5f099062\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c9580e2 elementor-widget-divider--view-line_text elementor-widget-divider--element-align-center elementor-widget elementor-widget-divider\" data-id=\"c9580e2\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t\t<span class=\"elementor-divider__text elementor-divider__element\">\n\t\t\t\tCOURSE\t\t\t\t<\/span>\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f6c24d6 elementor-nav-menu__text-align-center elementor-nav-menu__align-left elementor-nav-menu--dropdown-tablet elementor-nav-menu--toggle elementor-nav-menu--burger elementor-widget elementor-widget-nav-menu\" data-id=\"f6c24d6\" data-element_type=\"widget\" data-settings=\"{&quot;layout&quot;:&quot;vertical&quot;,&quot;submenu_icon&quot;:{&quot;value&quot;:&quot;&lt;svg class=\\&quot;e-font-icon-svg e-fas-caret-down\\&quot; viewBox=\\&quot;0 0 320 512\\&quot; xmlns=\\&quot;http:\\\/\\\/www.w3.org\\\/2000\\\/svg\\&quot;&gt;&lt;path d=\\&quot;M31.3 192h257.3c17.8 0 26.7 21.5 14.1 34.1L174.1 354.8c-7.8 7.8-20.5 7.8-28.3 0L17.2 226.1C4.6 213.5 13.5 192 31.3 192z\\&quot;&gt;&lt;\\\/path&gt;&lt;\\\/svg&gt;&quot;,&quot;library&quot;:&quot;fa-solid&quot;},&quot;toggle&quot;:&quot;burger&quot;}\" data-widget_type=\"nav-menu.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/ocw.nycu.edu.tw\/wp-content\/uploads\/elementor\/css\/custom-pro-widget-nav-menu.min.css?ver=1776064852\">\t\t\t<nav class=\"elementor-nav-menu--main elementor-nav-menu__container elementor-nav-menu--layout-vertical e--pointer-double-line e--animation-slide\">\n\t\t\t\t<ul id=\"menu-1-f6c24d6\" class=\"elementor-nav-menu sm-vertical\"><li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-121577\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/self-learning-courses-for-high-school-students\" class=\"elementor-item\">Self-learning courses for high school students<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-121578\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/pre-university-courses\" class=\"elementor-item\">Pre-University Courses<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5381\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\" class=\"elementor-item\">College of Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5377\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-engineering\" class=\"elementor-item\">College of Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5376\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-electrical-and-computer-engineering\" class=\"elementor-item\">College of Electrical and Computer Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5380\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-management\" class=\"elementor-item\">College of Management<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5375\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-computer-science\" class=\"elementor-item\">College of Computer Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5374\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biological-science-and-technology\" class=\"elementor-item\">College of Engineering Bioscience<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5379\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-humanities-and-social-sciences\" class=\"elementor-item\">College of Humanities Arts and Social Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5378\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-hakka-affair-culture\" class=\"elementor-item\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t\t<div class=\"elementor-menu-toggle\" role=\"button\" tabindex=\"0\" aria-label=\"\u9078\u55ae\u5207\u63db\" aria-expanded=\"false\">\n\t\t\t<svg aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--open e-font-icon-svg e-eicon-menu-bar\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M104 333H896C929 333 958 304 958 271S929 208 896 208H104C71 208 42 237 42 271S71 333 104 333ZM104 583H896C929 583 958 554 958 521S929 458 896 458H104C71 458 42 487 42 521S71 583 104 583ZM104 833H896C929 833 958 804 958 771S929 708 896 708H104C71 708 42 737 42 771S71 833 104 833Z\"><\/path><\/svg><svg aria-hidden=\"true\" role=\"presentation\" class=\"elementor-menu-toggle__icon--close e-font-icon-svg e-eicon-close\" viewBox=\"0 0 1000 1000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M742 167L500 408 258 167C246 154 233 150 217 150 196 150 179 158 167 167 154 179 150 196 150 212 150 229 154 242 171 254L408 500 167 742C138 771 138 800 167 829 196 858 225 858 254 829L496 587 738 829C750 842 767 846 783 846 800 846 817 842 829 829 842 817 846 804 846 783 846 767 842 750 829 737L588 500 833 258C863 229 863 200 833 171 804 137 775 137 742 167Z\"><\/path><\/svg>\t\t\t<span class=\"elementor-screen-only\">\u9078\u55ae<\/span>\n\t\t<\/div>\n\t\t\t\t\t<nav class=\"elementor-nav-menu--dropdown elementor-nav-menu__container\" aria-hidden=\"true\">\n\t\t\t\t<ul id=\"menu-2-f6c24d6\" class=\"elementor-nav-menu sm-vertical\"><li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-121577\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/self-learning-courses-for-high-school-students\" class=\"elementor-item\" tabindex=\"-1\">Self-learning courses for high school students<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-121578\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/pre-university-courses\" class=\"elementor-item\" tabindex=\"-1\">Pre-University Courses<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5381\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\" class=\"elementor-item\" tabindex=\"-1\">College of Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5377\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5376\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-electrical-and-computer-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Electrical and Computer Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5380\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-management\" class=\"elementor-item\" tabindex=\"-1\">College of Management<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5375\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-computer-science\" class=\"elementor-item\" tabindex=\"-1\">College of Computer Science<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5374\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biological-science-and-technology\" class=\"elementor-item\" tabindex=\"-1\">College of Engineering Bioscience<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5379\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-humanities-and-social-sciences\" class=\"elementor-item\" tabindex=\"-1\">College of Humanities Arts and Social Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-5378\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-hakka-affair-culture\" class=\"elementor-item\" tabindex=\"-1\">College of Hakka Affair Culture<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118070\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-law\" class=\"elementor-item\" tabindex=\"-1\">School of Law<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2.1.2 Linear D&hellip;<\/p>\n","protected":false},"featured_media":0,"parent":140179,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","format":"standard","meta":{"footnotes":""},"categories":[10999],"tags":[],"class_list":["post-140284","course_page","type-course_page","status-publish","format-standard","hentry","category-introduction-to-linear-algebra-113-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>2.1.2 Linear Dependence in Image Data - NYCU OCW<\/title>\n<meta name=\"description\" content=\"2.1.2 Linear Dependence in Image Data   https:\/\/youtu.be\/j4QiJ96wi7A      Back to Course Homepage       COURSE\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en\" \/>\n<meta property=\"og:locale\" content=\"zh_TW\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2.1.2 Linear Dependence in Image Data - NYCU OCW\" \/>\n<meta property=\"og:description\" content=\"2.1.2 Linear Dependence in Image Data   https:\/\/youtu.be\/j4QiJ96wi7A      Back to Course Homepage       COURSE\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en\" \/>\n<meta property=\"og:site_name\" content=\"NYCU OCW\" \/>\n<meta property=\"article:modified_time\" content=\"2025-06-30T08:27:14+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en\",\"url\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en\",\"name\":\"2.1.2 Linear Dependence in Image Data - NYCU OCW\",\"isPartOf\":{\"@id\":\"https:\/\/ocw.nycu.edu.tw\/#website\"},\"datePublished\":\"2025-06-30T08:25:48+00:00\",\"dateModified\":\"2025-06-30T08:27:14+00:00\",\"description\":\"2.1.2 Linear Dependence in Image Data https:\/\/youtu.be\/j4QiJ96wi7A Back to Course Homepage COURSE\",\"breadcrumb\":{\"@id\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en#breadcrumb\"},\"inLanguage\":\"zh-TW\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Homepage\",\"item\":\"https:\/\/ocw.nycu.edu.tw\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"ALL COURSE\",\"item\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"College of Science\",\"item\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Department of Applied Mathematics\",\"item\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\"},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"Introduction to Linear Algebra via Foreground-Background Separation Academic Year 113\",\"item\":\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\"},{\"@type\":\"ListItem\",\"position\":6,\"name\":\"2.1.2 Linear Dependence in Image Data\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/ocw.nycu.edu.tw\/#website\",\"url\":\"https:\/\/ocw.nycu.edu.tw\/\",\"name\":\"NYCU OCW\",\"description\":\"\u958b\u653e\u6559\u80b2\u662f\u73fe\u4ee3\u6559\u80b2\u601d\u6f6e\u7684\u4e00\u80a1\u4e3b\u6d41\uff0c\u570b\u5167\u5916\u5927\u5b78\u8fd1\u5e7e\u5e74\u9678\u7e8c\u958b\u653e\u6559\u80b2\u8cc7\u6e90\uff0c\u900f\u904e\u958b\u653e\u5f0f\u8ab2\u7a0b (OpenCourseWare, OCW)\u66a8\u5176\u61c9\u7528\u4e4b\u5efa\u7f6e\u5c07\u77e5\u8b58\u5206\u4eab\u65bc\u793e\u6703\u3002\",\"publisher\":{\"@id\":\"https:\/\/ocw.nycu.edu.tw\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/ocw.nycu.edu.tw\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-TW\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/ocw.nycu.edu.tw\/#organization\",\"name\":\"NYCU OCW\",\"url\":\"https:\/\/ocw.nycu.edu.tw\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-TW\",\"@id\":\"https:\/\/ocw.nycu.edu.tw\/#\/schema\/logo\/image\/\",\"url\":\"\",\"contentUrl\":\"\",\"caption\":\"NYCU OCW\"},\"image\":{\"@id\":\"https:\/\/ocw.nycu.edu.tw\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"2.1.2 Linear Dependence in Image Data - NYCU OCW","description":"2.1.2 Linear Dependence in Image Data   https:\/\/youtu.be\/j4QiJ96wi7A      Back to Course Homepage       COURSE","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en","og_locale":"zh_TW","og_type":"article","og_title":"2.1.2 Linear Dependence in Image Data - NYCU OCW","og_description":"2.1.2 Linear Dependence in Image Data   https:\/\/youtu.be\/j4QiJ96wi7A      Back to Course Homepage       COURSE","og_url":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en","og_site_name":"NYCU OCW","article_modified_time":"2025-06-30T08:27:14+00:00","twitter_card":"summary_large_image","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en","url":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en","name":"2.1.2 Linear Dependence in Image Data - NYCU OCW","isPartOf":{"@id":"https:\/\/ocw.nycu.edu.tw\/#website"},"datePublished":"2025-06-30T08:25:48+00:00","dateModified":"2025-06-30T08:27:14+00:00","description":"2.1.2 Linear Dependence in Image Data https:\/\/youtu.be\/j4QiJ96wi7A Back to Course Homepage COURSE","breadcrumb":{"@id":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en#breadcrumb"},"inLanguage":"zh-TW","potentialAction":[{"@type":"ReadAction","target":["https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113\/lafbs132_20250521-8-en#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Homepage","item":"https:\/\/ocw.nycu.edu.tw\/"},{"@type":"ListItem","position":2,"name":"ALL COURSE","item":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2"},{"@type":"ListItem","position":3,"name":"College of Science","item":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science"},{"@type":"ListItem","position":4,"name":"Department of Applied Mathematics","item":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics"},{"@type":"ListItem","position":5,"name":"Introduction to Linear Algebra via Foreground-Background Separation Academic Year 113","item":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/introduction-to-linear-algebra-via-foreground-background-separation-academic-year-113"},{"@type":"ListItem","position":6,"name":"2.1.2 Linear Dependence in Image Data"}]},{"@type":"WebSite","@id":"https:\/\/ocw.nycu.edu.tw\/#website","url":"https:\/\/ocw.nycu.edu.tw\/","name":"NYCU OCW","description":"\u958b\u653e\u6559\u80b2\u662f\u73fe\u4ee3\u6559\u80b2\u601d\u6f6e\u7684\u4e00\u80a1\u4e3b\u6d41\uff0c\u570b\u5167\u5916\u5927\u5b78\u8fd1\u5e7e\u5e74\u9678\u7e8c\u958b\u653e\u6559\u80b2\u8cc7\u6e90\uff0c\u900f\u904e\u958b\u653e\u5f0f\u8ab2\u7a0b (OpenCourseWare, OCW)\u66a8\u5176\u61c9\u7528\u4e4b\u5efa\u7f6e\u5c07\u77e5\u8b58\u5206\u4eab\u65bc\u793e\u6703\u3002","publisher":{"@id":"https:\/\/ocw.nycu.edu.tw\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ocw.nycu.edu.tw\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-TW"},{"@type":"Organization","@id":"https:\/\/ocw.nycu.edu.tw\/#organization","name":"NYCU OCW","url":"https:\/\/ocw.nycu.edu.tw\/","logo":{"@type":"ImageObject","inLanguage":"zh-TW","@id":"https:\/\/ocw.nycu.edu.tw\/#\/schema\/logo\/image\/","url":"","contentUrl":"","caption":"NYCU OCW"},"image":{"@id":"https:\/\/ocw.nycu.edu.tw\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=\/wp\/v2\/page\/140284","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=\/wp\/v2\/page"}],"about":[{"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=\/wp\/v2\/types\/course_page"}],"replies":[{"embeddable":true,"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=140284"}],"version-history":[{"count":4,"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=\/wp\/v2\/page\/140284\/revisions"}],"predecessor-version":[{"id":140292,"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=\/wp\/v2\/page\/140284\/revisions\/140292"}],"up":[{"embeddable":true,"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=\/wp\/v2\/page\/140179"}],"wp:attachment":[{"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=140284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=140284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ocw.nycu.edu.tw\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=140284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}