矩陣分析

Abstract

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