# A.2 线性代数

A.2.1 向量

一个n维向量的矩阵形式为：

其中

A.2.2 矩阵

由 m × n 个数aij排成的m行n列的数表称为m行n列的矩阵，简称m × n矩阵。记作：

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-65034cf35a8e2bf5a05f96beab53cdb52e8cb81f%2Fd8c638b3646036eae0d6a07039ef6d71.png?alt=media)

这m×n 个数称为矩阵**A**的元素，简称为元，数aij位于矩阵**A**的第i行第j列，称为矩阵**A**的(i,j)元，以数 aij为(i,j)元的矩阵可记为(aij)或(aij)m × n，m×n矩阵**A**也记作**Amn**。

A.2.3 运算

### 加法

矩阵的加法满足下列运算律(**A**，**B**，**C**都是同型矩阵)：

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-fd3f8eb4701471dccb699f9f73c5459de445c52a%2Fbb2db6f0befcd659a81db7d1165fcb47.png?alt=media)

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-8ba96c60a2b4d56c8046843055c5e35daa659977%2Fc2f2e45d67f8493a31005ec8d649c571.png?alt=media)

### 数乘

矩阵的数乘满足以下运算律：

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-85b1b390b571bf1fde37e8aa6596ace5eb371a18%2F0f2def2c8812ee7c6cd14639e1a9331a.png?alt=media)

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-0b4d05422681f84b30bfff5220a4e3de322bad87%2F29e85fb07d671511cc146aed35cfa8f7.png?alt=media)

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-c792541f6186d7e49df0a37d8dfa5a209a7640dd%2F31f744ef7611a1a0e8f6a0254f98aa4b.png?alt=media)

![](https://914753012-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-Mjx-LkXo6sfWzVc3cno%2Fuploads%2Fgit-blob-f93a478ea19d1745240bc81b54fbc42927b591c3%2F96ceaf2f2dc955e0d370051a59e58773.png?alt=media)

矩阵的加减法和矩阵的数乘合称矩阵的线性运算 \[8] 。

### 转置

把矩阵A的行和列互相交换所产生的矩阵称为A的转置矩阵，这一过程称为矩阵的转置
