標題: 矩陣分析Matrix Analysis 作者: 吳培元Open Education Office開放教育推動中心 公開日期: 2011 摘要: 課程首頁 本課程是由交通大學應用數學系提供。 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.課程目標/概述 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. 課程章節 內容綱要 General introduction of the course Basic operations on 2-by-2 matrices Row-equivalence, column-equivalence and unitary equivalence of matrices Similarity of matrices Jordan canonical form and spectral properties of matrices Rational form and nonderogatory matrices　 　 QR decomposition and singular value decomposition of matrices Perron-Frobenius theory of nonnegative matrices Discussions on mid-term homework problems Matrix inequalities Numerical ranges of matrices Matrix dilations Numerical ranges of matrices 課程書目 R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991. 評分標準 項目 百分比 上課表現、出席率 1/3 期中作業 1/3 期末作業 1/3授課對象：碩士班學生預備知識：Undergraduate linear algebra URI: http://ocw.nctu.edu.tw/course_detail.php?bgid=1&nid=263http://hdl.handle.net/11536/108379 Appears in Collections: Open Course Ware