《矩阵论及其应用》较为全面、系统地介绍了与工程技术联系密切的矩阵理论及其应用。全书共分为五章，分别介绍了线性空间与线性变换、λ-矩阵与Jordan标准形、矩阵分析及矩阵函数、矩阵微分方程、广义逆矩阵等内容。各章生面配有一定数量的习题，并在书末附有习题答案或提示。 

《矩阵论及其应用》可作为工科院校研究生和高年级本科生的教材，也可作为有关专业的教师及工程技术人员的参考书。

《矩阵论及其应用》由彭雄奇编著。

Chapter 1 Matrix Basics

1.1 Matrix Definition

1.2 Type of Matrices

1.3 Matrix Operations

1.4 Properties of Matrix Operations

1.5 Block Matrix

1.6 Elementary Row Operations

1.7 System of Linear Equations

Exercises

Chapter 2 Determinant

2.1 Definition of Determinant

2.2 Properties of Determinants

2.3 Cramer's Rule

Exercises

Chapter 3 Vector Spaces

3.1 Introduction

3.2 Field

3.3 Vector Space

3.4 Span

3.5 Linear Independence

3.6 Basis and Dimensions of Vector Space

3.7 Change of Basis

3.8 Fundamental Subspaces

Exercises

Chapter 4 Linear Transformation

4.1 Introduction

4.2 Linear Transformation

4.3 Matrix Representation of Linear Transformation

4.4 Linear Transformation with Basis Changes

4.5 Similarity

Exercises

Chapter 5 Eigenvalue and Eigenvector

5.1 Introduction

5.2 Eigenvalue and Eigenvector

5.3 Diagonalization

5.4 Computing Power of Matrix

5.5 Exponential of a Matrix

Exercises

Chapter 6 Orthogonality

6.1 Scalar Product in R

6.2 Orthogonality of" Null Space and Column Space

6.3 Orthogonal Set

6.4 Gram-Schmidt Orthogonalization Process

6.5 QR Decompositi0n

Exercises

Chapter 7 Special Matrices

7.1 Unitary and Orthogonal Matrices

7.2 Schur's TriangularizationTheorem

7.3 Normal Matrices

7.4 Hermitian Matrices

Exercises

Chapter 8 Singular Value Decomposition

8.1 Singular Va!ue Decomppsifion (SVD)

8.2 Polar Decomposition

8.3 Pseudo Inverse

8 4 The Jordan Form

Exercises

Refefences