{"id":20146,"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=20146"},"modified":"2022-08-24T10:53:43","modified_gmt":"2022-08-24T02:53:43","slug":"%e7%9f%a9%e9%99%a3%e5%88%86%e6%9e%90-matrix-analysis-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e5%9f%b9%e5%85%83%e8%80%81%e5%b8%ab","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course\/college-of-science\/am\/%e7%9f%a9%e9%99%a3%e5%88%86%e6%9e%90-matrix-analysis-%e6%87%89%e7%94%a8%e6%95%b8%e5%ad%b8%e7%b3%bb-%e5%90%b3%e5%9f%b9%e5%85%83%e8%80%81%e5%b8%ab","title":{"rendered":"\u77e9\u9663\u5206\u6790 Matrix Analysis | \u61c9\u7528\u6578\u5b78\u7cfb \u5433\u57f9\u5143\u8001\u5e2b"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"20146\" class=\"elementor elementor-20146\">\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 elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3742aef4 elementor-widget elementor-widget-breadcrumbs\" data-id=\"3742aef4\" data-element_type=\"widget\" data-widget_type=\"breadcrumbs.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\/plugins\/elementor-pro\/assets\/css\/widget-theme-elements.min.css\"><p id=\"breadcrumbs\"><span><span><a href=\"https:\/\/ocw.nycu.edu.tw\/\">Homepage<\/a><\/span><\/span><\/p>\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<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_9959\" 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                                                                <svg class=\"e-font-icon-svg e-fas-home\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M280.37 148.26L96 300.11V464a16 16 0 0 0 16 16l112.06-.29a16 16 0 0 0 15.92-16V368a16 16 0 0 1 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      <svg class=\"e-font-icon-svg e-fas-clipboard-list\" viewBox=\"0 0 384 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M336 64h-80c0-35.3-28.7-64-64-64s-64 28.7-64 64H48C21.5 64 0 85.5 0 112v352c0 26.5 21.5 48 48 48h288c26.5 0 48-21.5 48-48V112c0-26.5-21.5-48-48-48zM96 424c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm0-96c-13.3 0-24-10.7-24-24s10.7-24 24-24 24 10.7 24 24-10.7 24-24 24zm96-192c13.3 0 24 10.7 24 24s-10.7 24-24 24-24-10.7-24-24 10.7-24 24-24zm128 368c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16zm0-96c0 4.4-3.6 8-8 8H168c-4.4 0-8-3.6-8-8v-16c0-4.4 3.6-8 8-8h144c4.4 0 8 3.6 8 8v16z\"><\/path><\/svg>                                                            \n                                                            <span class=\"eael-tab-title  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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\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/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.<\/p><p>\u00a0<\/p><p><span style=\"color: #3366ff; font-size: 16px;\">\u8ab2\u7a0b\u7528\u66f8\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;\">\u70ba\u6c42\u5b78\u7fd2\u6210\u6548\u5b8c\u7f8e\uff0c\u8acb\u8cfc\u8cb7\u8ab2\u672c\uff01<\/span><\/p><p>\u00a0<\/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\">\u6388\u8ab2\u8001\u5e2b<\/th><td bgcolor=\"#EEEEEE\" width=\"518\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a0\u61c9\u7528\u6578\u5b78\u7cfb \u5433\u57f9\u5143\u8001\u5e2b<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u8ab2\u7a0b\u5b78\u5206<\/th><td class=\"\u3002\"><span style=\"color: #101010; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4, Arial; font-size: 16px;\">\u00a03\u5b78\u5206<\/span><\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5e74\u5ea6<\/th><td bgcolor=\"#EEEEEE\">\u00a0100\u5b78\u5e74\u5ea6<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u6388\u8ab2\u5c0d\u8c61<\/th><td>\u00a0\u78a9\u58eb\u73ed\u5b78\u751f<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u9810\u5099\u77e5\u8b58<\/th><td bgcolor=\"#EEEEEE\">\u00a0Undergraduate linear algebra<\/td><\/tr><tr><th style=\"text-align: center;\" nowrap=\"nowrap\" bgcolor=\"#FFF3DB\">\u8ab2\u7a0b\u63d0\u4f9b<\/th><td><i><\/i>\u00a0<a href=\"#video\">\u8ab2\u7a0b\u5f71\u97f3<\/a>\u00a0 \u00a0\u00a0<a href=\"#syllabus\">\u8ab2\u7a0b\u7db1\u8981<\/a>\u00a0 \u00a0 <a href=\"#calendar\">\u8ab2\u7a0b\u884c\u4e8b\u66c6<\/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-40\" class=\"tablepress tablepress-id-40\">\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\">\u7b2c\u4e00\u9031<\/td><td class=\"column-2\">General introduction of the course<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=20168\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e8c\u9031<\/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=23475\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\">\u7b2c\u4e8c\u9031<\/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=23481\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e09\u9031<\/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=23487\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\">\u7b2c\u4e09\u9031<\/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=23493\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\">\u7b2c\u56db\u9031<\/td><td class=\"column-2\">Similarity of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23499\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\">\u7b2c\u56db\u9031<\/td><td class=\"column-2\">Similarity of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23505\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e94\u9031<\/td><td class=\"column-2\">Similarity of matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23522\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\">\u7b2c\u516d\u9031<\/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=23528\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\">\u7b2c\u516d\u9031<\/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=23534\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\">\u7b2c\u4e03\u9031<\/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=23540\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e03\u9031<\/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=23546\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\">\u7b2c\u516b\u9031<\/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=23552\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\">\u7b2c\u516b\u9031<\/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=23558\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\">\u7b2c\u4e5d\u9031<\/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=23564\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\">\u7b2c\u4e5d\u9031<\/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=23570\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u9031<\/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=23576\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u9031<\/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=23582\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e00\u9031<\/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=23588\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e00\u9031<\/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=23594\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e8c\u9031<\/td><td class=\"column-2\">Matrix inequalities (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23600\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-23 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e8c\u9031<\/td><td class=\"column-2\">Matrix inequalities (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23606\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-24 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e09\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23612\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-25 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e09\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23618\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-26 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u56db\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23624\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-27 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u56db\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23630\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-28 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e94\u9031<\/td><td class=\"column-2\">Matrix dilations (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23636\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-29 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e94\u9031<\/td><td class=\"column-2\">Matrix dilations (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23642\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-30 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u516d\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23648\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-31 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u516d\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23654\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-32 even\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e03\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (1\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23660\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<tr class=\"row-33 odd\">\n\t<td class=\"column-1\">\u7b2c\u5341\u4e03\u9031<\/td><td class=\"column-2\">Numerical ranges of matrices (2\/2)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=23666\">\u7dda\u4e0a\u89c0\u770b<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-40 from cache --><\/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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