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