本书英文编写，较为全面、系统地介绍了矩阵理论的基本理论、方法和部分应用实例。全书共分为9章，内容包括：矩阵基本概念、线性空间与内积空间、线性变换、Jordan标准型、矩阵分解、Hermite矩阵与正定矩阵、范数理论与矩阵分析、广义逆理论及MATLAB软件入门。从理论、到软件、到应用实例，内容丰富，结构严谨。每一章有Reading的部分，各章后面配有一定数量的习题，供读者阅读开阔视野、理解内容和巩固知识。

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Chapter 1 
Review and Miscellanea: Basic Concepts in Linear Algebra 
We brie°y review， mostly without proof， the basic concepts and results taught in an ele- mentary linear algebra course. 
1.1 Matrix Concept and Special Matrices 
The term of matrix was ˉrst introduced by the British mathematician James Joseph Sylvester in 1890. The word \matrix" is derived from the Indo-European root mater， mean- ing \mother". Matrices are indeed the core of linear algebra. 
Firstly， we see the following two numbers tables(Table 1.1 and Table 1.2) in real life. Table 1.1 The price table of four kinds of cans in three supermarkets 
We can write it in brief in the form 
Table 1.2 The distances of three cities in China (km) 
We can write it in the brief form 
It is symmetric. 
Deˉnition 1.1.1(Matrix) An array of numbers (or symbols) in m rows and n columns 
is called an m ￡ n matrix. 
The notation 
or 
Usually， we denote