{"id":15372,"date":"2022-08-17T17:20:39","date_gmt":"2022-08-17T09:20:39","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=15372"},"modified":"2026-03-23T11:22:07","modified_gmt":"2026-03-23T03:22:07","slug":"lia001_2-5","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e7%b7%9a%e6%80%a7%e4%bb%a3%e6%95%b8%e4%b8%80-linear-algebra-i-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e8%8e%8a%e9%87%8d%e8%80%81%e5%b8%ab\/lia001_2-5","title":{"rendered":"2.5 The Change of Coordinate Matrix"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"15372\" class=\"elementor elementor-15372\">\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-3bba7640 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" 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data-id=\"37a8de18\" data-element_type=\"widget\" data-widget_type=\"penci-info-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"penci_info_box_20079\" class=\"penci-block-vc penci-info-box penci-ibox-float-left penci-view-default penci-shape-circle\">\r\n\t\t\t<div class=\"penci-ibox-inner\">\r\n\t\t\t\t\t\t\t\t<div class=\"penci-ibox-icon penci-ibox-icon--icon penci-icon penci-tibox-text\"><span class=\"penci-ibox-icon-fa\"><\/span><\/div>\t\t\t\t<div class=\"penci-ibox-content-wrap\">\r\n\t\t\t\t\t\t\t\t\t\t<h3 class=\"penci-ibox-title\">2.5 The Change of Coordinate Matrix\n<\/h3>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-68844b98 elementor-widget elementor-widget-video\" data-id=\"68844b98\" data-element_type=\"widget\" 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penci-disSticky penci-structure-20 elementor-section elementor-inner-section elementor-element elementor-element-69ce823d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"69ce823d\" 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-inner-column elementor-element elementor-element-b18f3da\" data-id=\"b18f3da\" 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-7c9e37db elementor-widget elementor-widget-penci-button\" data-id=\"7c9e37db\" 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 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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-261e13d1 elementor-widget elementor-widget-shortcode\" data-id=\"261e13d1\" 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-28\" class=\"tablepress tablepress-id-28\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">\u9031\u6b21<\/th><th class=\"column-2\">\u8ab2\u7a0b\u5167\u5bb9<\/th><th class=\"column-3\">\u8ab2\u7a0b\u5f71\u97f3<\/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\">\u7b2c\u4e00\u7ae0 Vector Space<br \/>\n1.1 Introduction<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15306\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.2 Vector Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15318\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.3 Subspaces(\u5b50\u7a7a\u9593)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15324\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.4 Linear Combinations and Systems of Linear Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15330\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.5 Linear Dependence and Linear Independence<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15336\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.6 Bases and Dimension (\u57fa\u5e95\u548c\u7dad\u5ea6)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15342\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Linear Transformations and Matrices<br \/>\n2.1 Linear Transformations, Null spaces, and ranges<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15348\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.2 The Matrix Representation of a Linear Transformation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15354\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.3 Composition of Linear Transformation and Matrix Multiplication<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15360\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.4 Invertibility and Isomorphisms<br \/>\n\u203b\u8a73\u898b\u52d8\u8aa4\u8868-1<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15366\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.5 The Change of Coordinate Matrix<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15372\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Elementary Matrix Operations and Systems of Linear Equations<br \/>\n3.1 Elementary Matrix Operations and Elementary Matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15378\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.2 The Rank of a Matrix and Matrix Inverses<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15384\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.3 Systems of Linear Equations-Theoretical Aspects<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15390\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.4 Systems of Linear Equations-Computational Aspects<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15396\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 Determinants<br \/>\n4.1 Determinants of Order 2<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15402\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.2 Determinants of Order w<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15408\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.2 Determinants of Order w-\u88dc\u5145<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15414\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.3 Properties of Determinants<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15420\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.4 Summary-Important Facts About Determinants<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15426\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.5 A Characterization of the Determinant<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15432\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-28 from cache 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