{"id":20161,"date":"2022-08-24T11:00:55","date_gmt":"2022-08-24T03:00:55","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=20161"},"modified":"2024-11-18T10:25:49","modified_gmt":"2024-11-18T02:25:49","slug":"matrix-analysis-department-of-applied-mathematics-prof-pei-yuan-wu","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/matrix-analysis-department-of-applied-mathematics-prof-pei-yuan-wu","title":{"rendered":"Matrix Analysis | Department of Applied Mathematics Prof. Pei Yuan Wu"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20161\" class=\"elementor elementor-20161\">\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-13d70f5a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"13d70f5a\" 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-373a1db9\" data-id=\"373a1db9\" 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-2c3529c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2c3529c0\" 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-128cf510\" data-id=\"128cf510\" 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-2f3e8fc1 elementor-widget elementor-widget-penci-info-box\" data-id=\"2f3e8fc1\" 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_97446\" 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<div class=\"penci-ibox-stit\">Matrix Analysis<\/div>\t\t\t\t\t<h3 class=\"penci-ibox-title\">\u77e9\u9663\u5206\u6790<\/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-76f0aacd elementor-widget elementor-widget-eael-adv-tabs\" data-id=\"76f0aacd\" data-element_type=\"widget\" data-widget_type=\"eael-adv-tabs.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t        <div id=\"eael-advance-tabs-76f0aacd\" class=\"eael-advance-tabs eael-tabs-horizontal eael-tab-auto-active\" data-tabid=\"76f0aacd\">\n            <div class=\"eael-tabs-nav\">\n                <ul class=\"eael-tab-inline-icon\">\n                                            <li id=\"home\" class=\"active-default eael-tab-item-trigger\" aria-selected=\"true\" data-tab=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"home-tab\" aria-expanded=\"false\">\n                            \n                                                                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12-12zm96 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm-96 96v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm-96 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm192 0v-40c0-6.6-5.4-12-12-12h-40c-6.6 0-12 5.4-12 12v40c0 6.6 5.4 12 12 12h40c6.6 0 12-5.4 12-12zm96-260v352c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V112c0-26.5 21.5-48 48-48h48V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h128V12c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v52h48c26.5 0 48 21.5 48 48zm-48 346V160H48v298c0 3.3 2.7 6 6 6h340c3.3 0 6-2.7 6-6z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  title-after-icon\">Course Calendar<\/span>                            \n                                                    <\/li>\n                                    <\/ul>\n            <\/div>\n            \n            <div class=\"eael-tabs-content\">\n\t\t        \n                    <div id=\"home-tab\" class=\"clearfix eael-tab-content-item active-default\" data-title-link=\"home-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><style type=\"text\/css\">\n.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/>.\u3002 {<br \/>\tfont-size: 18px;<br \/>}<br \/><\/style><\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u672c\u8ab2\u7a0b\u662f\u7531\u00a0<a href=\"https:\/\/www.math.nycu.edu.tw\/\" target=\"_blank\" rel=\"noopener\">\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78\u61c9\u7528\u6578\u5b78\u7cfb<\/a>\u00a0\u63d0\u4f9b\u3002<\/p><p style=\"margin-bottom: 10px; line-height: 28px; color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">The purpose of this course is to acquaint the students with some basic concepts in linear algebra and matrix analysis, which are most useful in applications. We will cover (1) the unitary-equivalence, similarity and congruence invariants of finite square matrices, (2) spectral properties of finite matrices, (3) Perron-Frobenius theory of nonnegative matrices, and numerical ranges of finite matrices.<br \/><br \/><\/p><p><span style=\"color: #3366ff; font-size: 16px;\">Textbook\uff1a<\/span><\/p><p><span style=\"font-size: 16px;\">R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.<br \/>R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.<\/span><\/p><p><span style=\"color: #ff00ff;\">For perfect learning results, please buy textbooks!<br \/><br \/><\/span><\/p><table style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\" border=\"1\"><tbody><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\" width=\"100\">Instructor(s)<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a0Department of Applied Mathematics Prof. Pei Yuan Wu<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Course Credits<\/th><td class=\"\u3002\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a03 Credits<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Academic Year<\/th><td bgcolor=\"#EEEEEE\">\u00a0100 Academic Year<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Level<\/th><td>\u00a0Master's Student<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Prior Knowledge<\/th><td bgcolor=\"#EEEEEE\">\u00a0Undergraduate linear algebra<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">Related Resources<\/th><td><i><\/i>\u00a0<a href=\"#video\">Course Video<\/a>\u00a0 \u00a0 <a href=\"#syllabus\">Course Syllabus<\/a>\u00a0 \u00a0 <a href=\"#calendar\">Course Calendar<\/a><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"video-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"video-tab\">\n\t\t\t\t        \t\t\t\t\t        <p>\n<table id=\"tablepress-41\" class=\"tablepress tablepress-id-41\">\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\">Week 01<\/td><td class=\"column-2\">General introduction of the course<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=20174&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">Week 02<\/td><td class=\"column-2\">Basic operations on 2-by-2 matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23679&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">Week 02<\/td><td class=\"column-2\">Basic operations on 2-by-2 matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23685&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">Week 03<\/td><td class=\"column-2\">Row-equivalence, column-equivalence and unitary equivalence of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23691&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">Week 03<\/td><td class=\"column-2\">Row-equivalence, column-equivalence and unitary equivalence of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23697&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">Week 04<\/td><td class=\"column-2\">Similarity of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23703&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">Week 04<\/td><td class=\"column-2\">Similarity of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23709&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">Week 05<\/td><td class=\"column-2\">Similarity of matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23715&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">Week 06<\/td><td class=\"column-2\">Jordan canonical form and spectral properties of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23721&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">Week 06<\/td><td class=\"column-2\">Jordan canonical form and spectral properties of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23727&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">Week 07<\/td><td class=\"column-2\">Rational form and nonderogatory matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23733&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">Week 07<\/td><td class=\"column-2\">Rational form and nonderogatory matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23739&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">Week 08<\/td><td class=\"column-2\">QR decomposition and singular value decomposition of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23745&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">Week 08<\/td><td class=\"column-2\">QR decomposition and singular value decomposition of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23751&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">Week 09<\/td><td class=\"column-2\">Perron-Frobenius theory of nonnegative matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23757&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">Week 09<\/td><td class=\"column-2\">Perron-Frobenius theory of nonnegative matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23763&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">Week 10<\/td><td class=\"column-2\">Perron-Frobenius theory of nonnegative matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23769&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">Week 10<\/td><td class=\"column-2\">Perron-Frobenius theory of nonnegative matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23777&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\">Week 11<\/td><td class=\"column-2\">Discussions on mid-term homework problems (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23783&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\">Week 11<\/td><td class=\"column-2\">Discussions on mid-term homework problems (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23789&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\">Week 12<\/td><td class=\"column-2\">Matrix inequalities (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23795&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\">Week 12<\/td><td class=\"column-2\">Matrix inequalities (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23801&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\">Week 13<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23807&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\">Week 13<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23813&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\">Week 14<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23824&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\">Week 14<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23830&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\">Week 15<\/td><td class=\"column-2\">Matrix dilations (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23836&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\">Week 15<\/td><td class=\"column-2\">Matrix dilations (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23842&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\">Week 16<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23848&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\">Week 16<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23854&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\">Week 17<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23862&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\">Week 17<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23868&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u00a0<\/p>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"syllabus-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"syllabus-tab\">\n\t\t\t\t        \t\t\t\t\t        <p class=\"title\"><strong>\u8ab2\u7a0b\u76ee\u6a19<\/strong><\/p><p class=\"text\">The purpose of this course is to acquaint the students with some basic concepts in linear algebra and matrix analysis, which are most useful in applications. We will cover<\/p><p class=\"text\">(1) the unitary-equivalence, similarity and congruence invariants of finite square matrices, <br \/>(2) spectral properties of finite matrices, <br \/>(3) Perron-Frobenius theory of nonnegative matrices, and numerical ranges of finite matrices.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u7ae0\u7bc0<\/strong><\/p><p>\u00a0<\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong> \u5167\u5bb9\u7db1\u8981<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">General introduction of the course<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Basic operations on 2-by-2 matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Row-equivalence, column-equivalence and unitary equivalence of matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Similarity of matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Jordan canonical form and spectral properties of matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Rational form and nonderogatory matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">QR decomposition and singular value decomposition of matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Perron-Frobenius theory of nonnegative matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Discussions on mid-term homework problems<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Matrix inequalities<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Numerical ranges of matrices<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">Matrix dilations<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">Numerical ranges of matrices<\/span><\/td><\/tr><\/tbody><\/table><p>\u00a0<\/p><p class=\"title\"><strong>\u8ab2\u7a0b\u66f8\u76ee<\/strong><\/p><p class=\"text\">R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985. <br \/>R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.<\/p><p>\u00a0<\/p><p class=\"title\"><strong>\u8a55\u5206\u6a19\u6e96<\/strong><\/p><table border=\"1\" cellspacing=\"0\"><tbody><tr class=\"stitle\"><td bgcolor=\"#FFF3DB\"><strong>\u9805\u76ee<\/strong><\/td><td bgcolor=\"#FFF3DB\"><strong>\u767e\u5206\u6bd4<\/strong><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u4e0a\u8ab2\u8868\u73fe\u3001\u51fa\u5e2d\u7387<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1\/3<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u671f\u4e2d\u4f5c\u696d<\/span><\/td><td style=\"padding: 5px;\" bgcolor=\"#f2f2ec\"><span class=\"text\">1\/3<\/span><\/td><\/tr><tr><td style=\"padding: 5px;\"><span class=\"text\">\u671f\u672b\u4f5c\u696d<\/span><\/td><td style=\"padding: 5px;\"><span class=\"text\">1\/3<\/span><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t        \n                    <div id=\"calendar-tab\" class=\"clearfix eael-tab-content-item inactive\" data-title-link=\"calendar-tab\">\n\t\t\t\t        \t\t\t\t\t        <p><span style=\"font-family: \u65b0\u7d30\u660e\u9ad4; font-size: 15px;\">\u672c\u8ab2\u7a0b\u884c\u4e8b\u66c6\u63d0\u4f9b\u8ab2\u7a0b\u9032\u5ea6\u8207\u8003\u8a66\u8cc7\u8a0a\u53c3\u8003\u3002<\/span><\/p><table style=\"font-style: normal; line-height: 20px; font-size: 15px; text-align: center;\" border=\"1\" cellspacing=\"0\"><tbody><tr><td bgcolor=\"#e4d8b0\" width=\"76\"><div style=\"text-align: center;\"><span style=\"color: #000000; font-weight: bold;\"><strong>\u5b78\u671f\u9031\u6b21<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"135\"><div style=\"text-align: center;\" align=\"center\"><span style=\"font-family: 'Times New Roman'; font-weight: bold;\"><strong>\u4e0a\u8ab2\u65e5\u671f<\/strong><\/span><\/div><\/td><td bgcolor=\"#e4d8b0\" width=\"440\"><div style=\"text-align: center; font-size: 15px; font-weight: bold;\"><strong>\u53c3\u8003\u8ab2\u7a0b\u9032\u5ea6<\/strong><\/div><\/td><\/tr><tr><td style=\"text-align: center;\"><p><span class=\"text\">\u7b2c\u4e00\u9031<\/span><\/p><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">09\/14<\/td><td style=\"text-align: left;\"><ul><li>General introduction of the course<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u4e8c\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">09\/19, 09\/21<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>Basic operations on 2-by-2 matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e09\u9031<\/span><\/td><td style=\"text-align: center;\">09\/26, 09\/28<\/td><td style=\"text-align: left;\"><ul><li>Row-equivalence, column-equivalence and unitary equivalence of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u56db\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">10\/03, 10\/05<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>Similarity of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e94\u9031<\/span><\/td><td style=\"text-align: center;\">10\/12<\/td><td style=\"text-align: left;\"><ul><li>Similarity of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516d\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">10\/17, 10\/19<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>Jordan canonical form and spectral properties of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e03\u9031<\/span><\/td><td style=\"text-align: center;\">10\/24, 10\/26<\/td><td style=\"text-align: left;\"><ul><li>Rational form and nonderogatory matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u516b\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">10\/31, 11\/02<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>QR decomposition and singular value decomposition of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u4e5d\u9031<\/span><\/td><td style=\"text-align: center;\">11\/07, 11\/09<\/td><td style=\"text-align: left;\"><ul><li>Perron-Frobenius theory of nonnegative matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">11\/14, 11\/16<\/td><td style=\"text-align: left;\" bgcolor=\"#F2F2EC\"><ul><li>Perron-Frobenius theory of nonnegative matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e00\u9031<\/span><\/td><td style=\"text-align: center;\">11\/21, 11\/23<\/td><td style=\"text-align: left;\"><ul><li>Discussions on mid-term homework problems<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u4e8c\u9031<\/span><\/td><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\">11\/28, 11\/30<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>Matrix inequalities<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e09\u9031<\/span><\/td><td style=\"text-align: center;\">12\/05, 12\/07<\/td><td style=\"text-align: left;\"><ul><li>Numerical ranges of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u56db\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\" bgcolor=\"#f2f2ec\">12\/12, 12\/14<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>Numerical ranges of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e94\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">12\/19, 12\/21<\/td><td style=\"text-align: left;\"><ul><li>Matrix dilations<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\" bgcolor=\"#f2f2ec\"><span class=\"text\">\u7b2c\u5341\u516d\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\" bgcolor=\"#f2f2ec\">12\/26, 12\/28<\/td><td style=\"text-align: left;\" bgcolor=\"#f2f2ec\"><ul><li>Numerical ranges of matrices<\/li><\/ul><\/td><\/tr><tr><td style=\"text-align: center;\"><span class=\"text\">\u7b2c\u5341\u4e03\u9031<\/span><\/td><td style=\"line-height: 20px; font-style: normal; font-size: 15px; text-align: center;\">01\/02, 01\/04<\/td><td style=\"text-align: left;\"><ul><li>Numerical ranges of matrices<\/li><\/ul><\/td><\/tr><\/tbody><\/table>\t\t\t\t                            <\/div>\n\t\t                    <\/div>\n        <\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-44bdbd33 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"44bdbd33\" 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 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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>Matrix Analysi&hellip;<\/p>\n","protected":false},"featured_media":20148,"parent":5277,"menu_order":0,"comment_status":"open","ping_status":"open","template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[242],"tags":[341,345,347,1113],"class_list":["post-20161","course_page","type-course_page","status-publish","format-standard","has-post-thumbnail","hentry","category-department-of-applied-mathematics-en","tag-label-all-course-en","tag-label-college-of-science-en","tag-label-am-en","tag-label-matrix-analysis-100-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matrix Analysis | Department of Applied Mathematics Prof. Pei Yuan Wu - NYCU OCW<\/title>\n<meta name=\"description\" content=\"Matrix Analysis \u77e9\u9663\u5206\u6790 Course Homepage Course Video Course Syllabus Course Calendar 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