MATLAB01:基本的数学运算与矩阵运算

今天药忘吃喽~ 2022-12-03 08:52 338阅读 0赞

转自：[https://blog.csdn.net/ncepu\_Chen/article/details/103034286][https_blog.csdn.net_ncepu_Chen_article_details_103034286]

**目录**

MATLAB基本语法

变量

变量名

保留变量不适合做变量名

变量名不应当覆盖内置函数名

变量类型

数字型变量的显示格式

MATLAB命令行

使用MATLAB进行数字运算

使用MATLAB计算数学表达式

MATLAB内置的数学函数

使用MATLAB进行矩阵运算

定义矩阵

向终端输入矩阵

使用冒号运算符创建向量

定义特殊矩阵

矩阵的索引

矩阵的操作

操作矩阵的运算符

操作矩阵的函数

学习一门技术最好的方式就是阅读官方文档,可以查看[MATLAB官方文档][MATLAB]

# MATLAB基本语法 #

## 变量 ##

*  MATLAB中的变量不需要声明.
 *  使用 `= `为变量赋值

### 变量名 ###

*  与大多数编程语言相同,MATLAB中的变量名是大小写敏感的.
 *  变量名只能由\[`0~9`,`a~z`,`A~z`,`_`\]组成,且变量名不能以数字开头.

### 保留变量不适合做变量名 ###

MATLAB中有一些变量有其具体意义,不适合用作变量名.

<table style="width:546px;"> 
 <thead> 
  <tr> 
   <th>变量</th> 
   <th style="width:455px;">意义</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td><span style="color:#f33b45;"><code>ans</code></span></td> 
   <td style="width:455px;">上一句的运算的结果</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>i</code></span>和<span style="color:#f33b45;"><code>j</code></span></td> 
   <td style="width:455px;">复数算子</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>Inf</code></span></td> 
   <td style="width:455px;">无穷<img alt="\infty" src="https://private.codecogs.com/gif.latex?%5Cinfty"></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>eps</code></span></td> 
   <td style="width:455px;">浮点相对精度,即1.0到下一个浮点数之间的距离(值为2.2204e-16)</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>NaN</code></span></td> 
   <td style="width:455px;">非数字</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>pi</code></span></td> 
   <td style="width:455px;">圆周率<img alt="\pi" src="https://private.codecogs.com/gif.latex?%5Cpi"></td> 
  </tr> 
 </tbody> 
</table>

除此以外,使用`iskeyword`命令可以查看MATLAB语言所有的关键字,这些关键字也不允许被用作变量名.

### 变量名不应当覆盖内置函数名 ###

在MATLAB中,变量的调用优先级(calling priority)高于函数,因此变量名不应该覆盖内置函数.

![MATLAB的调用优先级][MATLAB 1]

cos='This string.';
    cos(8)		% 对字符串进行索引取值,得到'r'

若某函数被变量名所覆盖,则调用`clear <变量名>`可以取消绑定在该函数名上的变量名

clear cos	% 清除绑定在cos上的变量
    cos(8)		% 调用内置余弦函数运算得到-0.1455

> `clear`是一个比较危险的命令,因为该命令后若不加参数,则表示清除当前工作区内的所有变量.

### 变量类型 ###

MATLAB中的变量类型有: `logical`,`char`,`numeric`,`cell`,`struct`以及由他们组成的数组或矩阵.

![MATLAB中的变量类型][MATLAB 2]

### 数字型变量的显示格式 ###

我们直接定义的数字型变量,默认是以`double`形式存储的.

我们可以通过`format <显示格式>`改变数字型变量的显示格式.

<table> 
 <thead> 
  <tr> 
   <th>显示格式</th> 
   <th style="width:626px;">说明</th> 
   <th style="width:208px;">例子</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td><span style="color:#f33b45;"><code>short</code></span></td> 
   <td style="width:626px;">短定点格式.显示小数点后4位</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>3.1416</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>long</code></span></td> 
   <td style="width:626px;">长定点格式.对<span style="color:#f33b45;"><code>double</code></span>类型变量显示小数点后15位,对<span style="color:#f33b45;"><code>float</code></span>类型变量显示小数点后7位.</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>3.141592653589793</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>shortE</code></span></td> 
   <td style="width:626px;">短科学计数法,显示小数点后4位.并带有科学计数法标记.</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>3.1416e+00</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>longE</code></span></td> 
   <td style="width:626px;">长科学计数法.对<span style="color:#f33b45;"><code>double</code></span>类型变量显示小数点后15位,对<span style="color:#f33b45;"><code>float</code></span>类型变量显示小数点后7位.并带有科学计数法标记.</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>3.141592653589793e+00</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>bank</code></span></td> 
   <td style="width:626px;">银行格式.显示小数点后2位.</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>3.14</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>hex</code></span></td> 
   <td style="width:626px;">十六进制格式.</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>400921fb54442d18</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>rat</code></span></td> 
   <td style="width:626px;">比例格式</td> 
   <td style="width:208px;"><span style="color:#f33b45;"><code>355/113</code></span></td> 
  </tr> 
 </tbody> 
</table>

## MATLAB命令行 ##

1.  使用行尾`;`抑制输出: 在一行命令后使用`;`抑制输出,否则运算结果将被显示在终端上.
2.  其他实用的命令:
    
    <table style="width:356px;"> 
     <thead> 
      <tr> 
       <th style="width:103px;">命令</th> 
       <th style="width:250px;">作用</th> 
      </tr> 
     </thead> 
     <tbody> 
      <tr> 
       <td style="width:103px;"><span style="color:#f33b45;"><code>clc</code></span></td> 
       <td style="width:250px;">清除终端的输出</td> 
      </tr> 
      <tr> 
       <td style="width:103px;"><span style="color:#f33b45;"><code>clear</code></span></td> 
       <td style="width:250px;">清除当前工作区内所有变量</td> 
      </tr> 
      <tr> 
       <td style="width:103px;"><span style="color:#f33b45;"><code>who</code></span></td> 
       <td style="width:250px;">以简略格式显示工作区内所有变量</td> 
      </tr> 
      <tr> 
       <td style="width:103px;"><span style="color:#f33b45;"><code>whos</code></span></td> 
       <td style="width:250px;">以复杂格式显示工作区内所有变量</td> 
      </tr> 
     </tbody> 
    </table>

# 使用MATLAB进行数字运算 #

## 使用MATLAB计算数学表达式 ##

*  MATLAB常见运算符有: `+`,`-`,`*`,`/`,`^`.
 *  数学表达式被计算后,其值被存入变量`ans`.
 *  运算的优先级规则:
    
     *  同等优先级下从左向右运算.
     *  优先级顺序(从高到低)
        
        1.  括号`()`
        2.  乘方`^`
        3.  乘除法`*`,`/`
        4.  加减法`+`,`-`

下面例子演示了数学表达式求值:

<table style="width:429px;"> 
 <tbody> 
  <tr> 
   <td style="width:234px;"><strong>待求数学表达式</strong></td> 
   <td style="width:192px;"><strong>MATLAB命令</strong></td> 
  </tr> 
  <tr> 
   <td style="width:234px;"><img alt="\cos (\sqrt{\frac{(1+2+3+4)^{3}}{5}})" src="https://private.codecogs.com/gif.latex?%5Ccos%20%28%5Csqrt%7B%5Cfrac%7B%281&amp;plus;2&amp;plus;3&amp;plus;4%29%5E%7B3%7D%7D%7B5%7D%7D%29"></td> 
   <td style="width:192px;"><span style="color:#f33b45;">cos(sqrt((1+2+3+4)^3/5))</span></td> 
  </tr> 
  <tr> 
   <td style="width:234px;"><img alt="\sin \left ( \sqrt{\pi } \right )+\ln \left ( \tan \left ( 1 \right ) \right )" src="https://private.codecogs.com/gif.latex?%5Csin%20%5Cleft%20%28%20%5Csqrt%7B%5Cpi%20%7D%20%5Cright%20%29&amp;plus;%5Cln%20%5Cleft%20%28%20%5Ctan%20%5Cleft%20%28%201%20%5Cright%20%29%20%5Cright%20%29"></td> 
   <td style="width:192px;"><span style="color:#f33b45;">sin(sqrt(pi))+log(tan(1))</span></td> 
  </tr> 
  <tr> 
   <td style="width:234px;"><img alt="2^{3.5\times 1.7}" src="https://private.codecogs.com/gif.latex?2%5E%7B3.5%5Ctimes%201.7%7D"></td> 
   <td style="width:192px;"><span style="color:#f33b45;"><code>2^(3.5*1.7)</code></span></td> 
  </tr> 
  <tr> 
   <td style="width:234px;"><img alt="e^{\sin \left ( 10 \right )}" src="https://private.codecogs.com/gif.latex?e%5E%7B%5Csin%20%5Cleft%20%28%2010%20%5Cright%20%29%7D"></td> 
   <td style="width:192px;"><span style="color:#f33b45;"><code>exp(sin(10))</code></span></td> 
  </tr> 
 </tbody> 
</table>

##    MATLAB内置的数学函数 ##

*  [MATLAB内置的算数运算函数][MATLAB 3]
    
     *  基本运算:
        
         *  加: `+``,``sum``,``cumsum``,``movsum`
         *  减: `-,``diff`
         *  乘: `.*`,`*`,`prod`,`cumprod`
         *  除: `./`,`.\`,`/`,`\`
         *  乘方: `.^`,`^`
     *  取模运算: `mod`,`rem`,`idivide`,`ceil`,`fix`,`floor`,`round`
 *  [MATLAB内置的三角运算函数][MATLAB 4]
    
     *  正弦: `sin`,`sind`,`sinpi`,`asin`,`asind`,`sinh`,`asinh`
     *  余弦: `cos`,`cosd`,`cospi`,`acos`,`acosd`,`cosh`,`acosh`
     *  正切: `tan`,`tand`,`atan`,`atand`,`atan2`,`atan2d`,`tanh`,`atanh`
     *  余割: `csc`,`cscd`,`acsc`,`acscd`,`csch`,`acsch`
     *  正割: `sec`,`secd`,`asec`,`asecd`,`sech`,`asech`
     *  余切: `cot`,`cotd`,`acot`,`acotd`,`coth`,`acoth`
     *  斜边: `hypot`
     *  转换: `deg2rad`,`rad2deg`,`cart2pol`,`cart2sph`,`pol2cart`,`sph2cart`
 *  [MATLAB内置的指数对数函数][MATLAB 5]: `exp`,`expm1`,`log`,`log10`,`log1p`,`log2`,`nextpow2`,`nthroot`,`pow2`,`reallog`,`realpow`,`realsqrt`,`sqrt`
 *  [MATLAB内置的复函数][MATLAB 6]: `abs`,`angle`,`complex`,`conj`,`cplxpair`,`i`,`imag`,`isreal`,`j`,`real`,`sign`,`unwrap`

# 使用MATLAB进行矩阵运算 #

## 定义矩阵 ##

### 向终端输入矩阵 ###

在MATLAB中,使用`[]`将待输入的矩阵内容括起来,使用空格或逗号`,`分隔行内变量,使用`;`分隔每一行.

下面例子演示了矩阵的定义:

<table style="width:391px;"> 
 <thead> 
  <tr> 
   <th style="width:217px;">MATLAB命令</th> 
   <th style="width:171px;">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;得到的矩阵</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td style="width:217px;"><span style="color:#f33b45;"><code>[1 2 3 4]</code></span></td> 
   <td style="width:171px;">&nbsp; &nbsp; &nbsp;<img alt="\begin{bmatrix} 1 &amp; 2 &amp; 3 &amp;4 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%20%264%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:217px;"><span style="color:#f33b45;"><code>[1; 2; 3; 4]</code></span></td> 
   <td style="width:171px;">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img alt="\begin{bmatrix} 1\\ 2\\ 3\\ 4 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%5C%5C%202%5C%5C%203%5C%5C%204%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:217px;"><span style="color:#f33b45;"><code>[1 21 6; 5 17 9; 31 2 7]</code></span></td> 
   <td style="width:171px;">&nbsp; &nbsp; &nbsp;&nbsp;<img alt="\begin{bmatrix} 1 &amp; 21&amp;6 \\ 5 &amp; 17&amp; 9\\ 31&amp; 2 &amp; 7 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%2021%266%20%5C%5C%205%20%26%2017%26%209%5C%5C%2031%26%202%20%26%207%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
 </tbody> 
</table>

### 使用冒号运算符创建向量 ###

使用冒号运算符`:`可以创建一个长向量,其语法如下:

<table> 
 <thead> 
  <tr> 
   <th>冒号表达式</th> 
   <th>得到的结果</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td><span style="color:#f33b45;"><code>j:k</code></span></td> 
   <td><img alt="\begin{bmatrix} j, &amp; j+1, &amp;j+2, &amp;..., &amp;j+m \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%20j%2C%20%26%20j&amp;plus;1%2C%20%26j&amp;plus;2%2C%20%26...%2C%20%26j&amp;plus;m%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>j:i:k</code></span></td> 
   <td><img alt="\begin{bmatrix} j, &amp; j+i, &amp;j+2i, &amp;..., &amp;j+m*i \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%20j%2C%20%26%20j&amp;plus;i%2C%20%26j&amp;plus;2i%2C%20%26...%2C%20%26j&amp;plus;m*i%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
 </tbody> 
</table>

下面例子演示了冒号运算符的使用:

<table style="width:504px;"> 
 <thead> 
  <tr> 
   <th style="width:220px;">MATLAB语句</th> 
   <th style="width:281px;">得到的结果</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td style="width:220px;"><span style="color:#f33b45;"><code>1:5</code></span></td> 
   <td style="width:281px;">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img alt="\begin{bmatrix} 1 &amp; 2 &amp; 3 &amp;4 &amp;5 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%20%264%20%265%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:220px;"><span style="color:#f33b45;"><code>1:2:5</code></span></td> 
   <td style="width:281px;">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img alt="\begin{bmatrix} 1 &amp; 3 &amp;5 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%203%20%265%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:220px;"><span style="color:#f33b45;"><code>[1:5; 2:3:15; -2:0.5:0]</code></span></td> 
   <td style="width:281px;">&nbsp;&nbsp;<img alt="\begin{bmatrix} 1 &amp; 2&amp;3 &amp;4 &amp;5 \\ 2&amp;5 &amp;8 &amp;11 &amp;14 \\ -2&amp;-1.5 &amp;-1 &amp;-0.5 &amp;0 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%202%263%20%264%20%265%20%5C%5C%202%265%20%268%20%2611%20%2614%20%5C%5C%20-2%26-1.5%20%26-1%20%26-0.5%20%260%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:220px;"><span style="color:#f33b45;"><code>'a':2:'z'</code></span></td> 
   <td style="width:281px;"><span style="color:#f33b45;"><code>'acegikmoqsuwy'</code></span></td> 
  </tr> 
 </tbody> 
</table>

### 定义特殊矩阵 ###

下列命令可以定义特殊矩阵

<table style="width:528px;"> 
 <thead> 
  <tr> 
   <th style="width:166px;">命令</th> 
   <th style="width:359px;">得到的结果</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td style="width:166px;"><span style="color:#f33b45;"><code>eye(n)</code></span></td> 
   <td style="width:359px;">得到一个<img alt="n\times n" src="https://private.codecogs.com/gif.latex?n%5Ctimes%20n">的单位矩阵</td> 
  </tr> 
  <tr> 
   <td style="width:166px;"><span style="color:#f33b45;"><code>zeros(n1, n2)</code></span></td> 
   <td style="width:359px;">得到一个<img alt="n_{1} \times n_{2}" src="https://private.codecogs.com/gif.latex?n_%7B1%7D%20%5Ctimes%20n_%7B2%7D">的全0矩阵</td> 
  </tr> 
  <tr> 
   <td style="width:166px;"><span style="color:#f33b45;"><code>ones(n1, n2)</code></span></td> 
   <td style="width:359px;">得到一个<img alt="n_{1} \times n_{2}" src="https://private.codecogs.com/gif.latex?n_%7B1%7D%20%5Ctimes%20n_%7B2%7D">的全1矩阵</td> 
  </tr> 
  <tr> 
   <td style="width:166px;"><span style="color:#f33b45;"><code>diag(vector)</code></span></td> 
   <td style="width:359px;">得到一个以向量<span style="color:#f33b45;"><code>vector</code></span>中内容为对角线的对角矩阵</td> 
  </tr> 
 </tbody> 
</table>

## 矩阵的索引 ##

*  MATLAB中的矩阵是以列先序存储的.且索引下标从1开始.
 *  矩阵有两种索引方式: 按一维索引和按二维索引.对于一个一般的矩阵,其索引顺序如下:

![\\begin\{bmatrix\} 1or \\left ( 1,1 \\right )& 4or \\left ( 1,2 \\right ) & 7or \\left ( 1,3 \\right )\\\\ 2or \\left ( 2,1 \\right )& 5or \\left ( 2,2\\right )& 8or \\left ( 2,3 \\right )\\\\ 3or \\left ( 3,1 \\right )&6or \\left ( 3,2 \\right ) & 9or \\left ( 3,3 \\right )\\end\{bmatrix\}][begin_bmatrix_ 1or _left _ 1_1 _right _ 4or _left _ 1_2 _right _ _ 7or _left _ 1_3 _right _ 2or _left _ 2_1 _right _ 5or _left _ 2_2_right _ 8or _left _ 2_3 _right _ 3or _left _ 3_1 _right _6or _left _ 3_2 _right _ _ 9or _left _ 3_3 _right _end_bmatrix]

*  矩阵的索引可以使用冒号`:`,表示选取所有行或所有列.
 *  矩阵的索引可以是一个或两个向量,表示选中向量内的所有行或所有列.

下面例子演示了矩阵索引的规则:

<table> 
 <thead> 
  <tr> 
   <th>原矩阵</th> 
   <th style="width:118px;">索引</th> 
   <th style="width:154px;">得到的结果</th> 
   <th style="width:376px;">解释</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td><img alt="A = \begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \\ 7&amp; 8 &amp;9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5C%5C%207%26%208%20%269%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:118px;"><span style="color:#f33b45;"><code>A(8)</code></span></td> 
   <td style="width:154px;">6</td> 
   <td style="width:376px;">取矩阵第8个元素</td> 
  </tr> 
  <tr> 
   <td><img alt="A = \begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \\ 7&amp; 8 &amp;9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5C%5C%207%26%208%20%269%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:118px;"><span style="color:#f33b45;"><code>A([1 3 5])</code></span></td> 
   <td style="width:154px;"><img alt="\begin{bmatrix} 1 &amp; 7&amp; 5 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%207%26%205%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:376px;">分别取矩阵第<span style="color:#f33b45;"><code>[1 3 5]</code></span>个元素放入新矩阵的对应位置</td> 
  </tr> 
  <tr> 
   <td><img alt="A = \begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \\ 7&amp; 8 &amp;9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5C%5C%207%26%208%20%269%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:118px;"><span style="color:#f33b45;"><code>A([1 2; 3 4])</code></span></td> 
   <td style="width:154px;"><img alt="\begin{bmatrix} 1 &amp; 4\\ 7 &amp;2\end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%204%5C%5C%207%20%262%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:376px;">分别取矩阵第<span style="color:#f33b45;"><code>[1 2; 3 4]</code></span>个元素放入新矩阵的对应位置</td> 
  </tr> 
  <tr> 
   <td><img alt="A = \begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \\ 7&amp; 8 &amp;9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5C%5C%207%26%208%20%269%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:118px;"><span style="color:#f33b45;"><code>A(3,2)</code></span></td> 
   <td style="width:154px;">8</td> 
   <td style="width:376px;">取矩阵第3行第2列的元素</td> 
  </tr> 
  <tr> 
   <td><img alt="A = \begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \\ 7&amp; 8 &amp;9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5C%5C%207%26%208%20%269%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:118px;"><span style="color:#f33b45;"><code>A([1,2], :)</code></span></td> 
   <td style="width:154px;"><img alt="\begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:376px;">取矩阵第<span style="color:#f33b45;"><code>[1 2]</code></span>行和所有列的交叉项</td> 
  </tr> 
  <tr> 
   <td><img alt="A = \begin{bmatrix} 1 &amp; 2 &amp; 3\\ 4&amp; 5 &amp;6 \\ 7&amp; 8 &amp;9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%204%26%205%20%266%20%5C%5C%207%26%208%20%269%20%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:118px;"><span style="color:#f33b45;"><code>A([1 3], [1 2])</code></span></td> 
   <td style="width:154px;"><img alt="\begin{bmatrix} 1 &amp; 2\\ 7 &amp;8\end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%202%5C%5C%207%20%268%5Cend%7Bbmatrix%7D"></td> 
   <td style="width:376px;">取矩阵第<span style="color:#f33b45;"><code>[1 3]</code></span>行和第<span style="color:#f33b45;"><code>[1 2]</code></span>列的交叉项</td> 
  </tr> 
 </tbody> 
</table>

## 矩阵的操作 ##

### 操作矩阵的运算符 ###

<table> 
 <thead> 
  <tr> 
   <th>运算符</th> 
   <th style="width:237px;">操作</th> 
   <th style="width:93px;">形式</th> 
   <th style="width:336px;">例子</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td><span style="color:#f33b45;"><code>+</code></span></td> 
   <td style="width:237px;">矩阵与向量相加</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A+b</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] + 2 = [8 5]</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>-</code></span></td> 
   <td style="width:237px;">矩阵与向量相减</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A-b</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] - 2 = [4 1]</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>+</code></span></td> 
   <td style="width:237px;">矩阵与矩阵对应位置相加</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A+B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] + [4 8] = [10 11]</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>-</code></span></td> 
   <td style="width:237px;">矩阵与矩阵对应位置相减</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A-B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] - [4 8] = [2 -5]</code></span></td> 
  </tr> 
  <tr> 
   <td>&nbsp;</td> 
   <td style="width:237px;">&nbsp;</td> 
   <td style="width:93px;">&nbsp;</td> 
   <td style="width:336px;">&nbsp;</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>*</code></span></td> 
   <td style="width:237px;">矩阵与矩阵相乘</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A*B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] * [4 8]' = 48</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>.*</code></span></td> 
   <td style="width:237px;">矩阵与矩阵对应位置相乘</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A.*B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] * [4 8] = [24 24]</code></span></td> 
  </tr> 
  <tr> 
   <td>&nbsp;</td> 
   <td style="width:237px;">&nbsp;</td> 
   <td style="width:93px;">&nbsp;</td> 
   <td style="width:336px;">&nbsp;</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>/</code></span></td> 
   <td style="width:237px;">矩阵与矩阵右除(等价于<span style="color:#f33b45;"><code>A*inv(B)</code></span>)</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A/B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] / [4 8] = 0.6</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>\</code></span></td> 
   <td style="width:237px;">矩阵与矩阵左除(等价于<span style="color:#f33b45;"><code>inv(A)*B</code></span>)</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A\B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] / [4 8] = [0.06667 1.3333; 0 0]</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>./</code></span></td> 
   <td style="width:237px;">矩阵与矩阵对应位置右除</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A./B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] ./ [4 8] = [1.5 0.375]</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>.\</code></span></td> 
   <td style="width:237px;">矩阵与矩阵对应位置左除</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A.\B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[6 3] .\ [4 8]' = [0.6667 2.6667]</code></span></td> 
  </tr> 
  <tr> 
   <td>&nbsp;</td> 
   <td style="width:237px;">&nbsp;</td> 
   <td style="width:93px;">&nbsp;</td> 
   <td style="width:336px;">&nbsp;</td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>^</code></span></td> 
   <td style="width:237px;">矩阵与向量乘方</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A^b</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[1 2; 3 4]^3 = [37 54; 81 118]</code></span></td> 
  </tr> 
  <tr> 
   <td><span style="color:#f33b45;"><code>.^</code></span></td> 
   <td style="width:237px;">矩阵与矩阵对应位置乘方</td> 
   <td style="width:93px;"><span style="color:#f33b45;"><code>A.^B</code></span></td> 
   <td style="width:336px;"><span style="color:#f33b45;"><code>[1 2; 3 4].^[1 2; 3 4] = [1 4; 27 256]</code></span></td> 
  </tr> 
 </tbody> 
</table>

### 操作矩阵的函数 ###

下面对矩阵  
                                                                                     ![A = \\begin\{bmatrix\} 1 & 2 & 3\\\\ 0& 5 &6 \\\\ 7& 0 &9 \\end\{bmatrix\}][A _ _begin_bmatrix_ 1 _ 2 _ 3_ 0_ 5 _6 _ 7_ 0 _9 _end_bmatrix]

进行操作以演示操作矩阵的常见函数

<table> 
 <thead> 
  <tr> 
   <th style="width:211px;">函数</th> 
   <th style="width:269px;">作用</th> 
   <th style="width:202px;">例子</th> 
   <th style="width:220px;">结果</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>max(A, [], dim)</code></span></td> 
   <td style="width:269px;">获取矩阵<span style="color:#f33b45;"><code>A</code></span>的<span style="color:#f33b45;"><code>dim</code></span>维度上的最大值</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>max(A, [], 1)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 7 &amp;5&amp; 9 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%207%20%265%26%209%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>min(A, [], dim)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>的<code>dim</code>维度上的最小值</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>min(A, [], 2)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 1 &amp; 0&amp; 0 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%200%26%200%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>sum(A, dim)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>的<code>dim</code>维度上的和</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>sum(A, 1)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 8 &amp; 7&amp; 18 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%208%20%26%207%26%2018%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>mean(A, dim)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>的<code>dim</code>维度上的平均值</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>mean(A, 1)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 2.6667 &amp; 2.3333&amp; 6.0000 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%202.6667%20%26%202.3333%26%206.0000%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>sort(A, dim, direction)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>的<code>dim</code>维度上按<code>direction</code>顺序排序结果</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>sort(A, 1, 'descend')</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 7 &amp; 5 &amp; 9\\ 1&amp; 2 &amp;6 \\ 0&amp; 0 &amp;3 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%207%20%26%205%20%26%209%5C%5C%201%26%202%20%266%20%5C%5C%200%26%200%20%263%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>sortrows(A, column)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>按照每行第<code>column</code>个元素升序排序结果.</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>sortrows(A, 2)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 7 &amp; 0 &amp; 9\\ 1&amp; 2 &amp;3\\ 0&amp; 5 &amp;6 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%207%20%26%200%20%26%209%5C%5C%201%26%202%20%263%5C%5C%200%26%205%20%266%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>size(A, dim)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>的<code>dim</code>维度上的形状.若不指定<code>dim</code>,则返回整个矩阵的形状.</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>size(A)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 3 &amp; 3 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%203%20%26%203%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
  <tr> 
   <td style="width:211px;"><span style="color:#f33b45;"><code>find(A, n)</code></span></td> 
   <td style="width:269px;">获取矩阵<code>A</code>前<code>n</code>个非零元素的索引</td> 
   <td style="width:202px;"><span style="color:#f33b45;"><code>find(A,5)</code></span></td> 
   <td style="width:220px;"><img alt="\begin{bmatrix} 1 &amp; 3&amp; 4&amp; 5&amp; 7 \end{bmatrix}" src="https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201%20%26%203%26%204%26%205%26%207%20%5Cend%7Bbmatrix%7D"></td> 
  </tr> 
 </tbody> 
</table>

> 对于上面这些函数,除第一个参数以外,其它参数都是可选的.

[https_blog.csdn.net_ncepu_Chen_article_details_103034286]: https://blog.csdn.net/ncepu_Chen/article/details/103034286
[MATLAB]: https://ww2.mathworks.cn/help/matlab/getting-started-with-matlab.html?lang=en
[MATLAB 1]: /images/20221123/7eac107b43324c649575adbd481f8bb4.png
[MATLAB 2]: /images/20221123/4bd757d684a6446b95cbe9b0f6ca497f.png
[MATLAB 3]: https://www.mathworks.com/help/matlab/arithmetic.html
[MATLAB 4]: http://www.mathworks.com/help/matlab/trigonometry.html
[MATLAB 5]: https://www.mathworks.com/help/matlab/exponents-and-logarithms.html
[MATLAB 6]: https://www.mathworks.com/help/matlab/complex-numbers.html
[begin_bmatrix_ 1or _left _ 1_1 _right _ 4or _left _ 1_2 _right _ _ 7or _left _ 1_3 _right _ 2or _left _ 2_1 _right _ 5or _left _ 2_2_right _ 8or _left _ 2_3 _right _ 3or _left _ 3_1 _right _6or _left _ 3_2 _right _ _ 9or _left _ 3_3 _right _end_bmatrix]: https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%201or%20%5Cleft%20%28%201%2C1%20%5Cright%20%29%26%204or%20%5Cleft%20%28%201%2C2%20%5Cright%20%29%20%26%207or%20%5Cleft%20%28%201%2C3%20%5Cright%20%29%5C%5C%202or%20%5Cleft%20%28%202%2C1%20%5Cright%20%29%26%205or%20%5Cleft%20%28%202%2C2%5Cright%20%29%26%208or%20%5Cleft%20%28%202%2C3%20%5Cright%20%29%5C%5C%203or%20%5Cleft%20%28%203%2C1%20%5Cright%20%29%266or%20%5Cleft%20%28%203%2C2%20%5Cright%20%29%20%26%209or%20%5Cleft%20%28%203%2C3%20%5Cright%20%29%5Cend%7Bbmatrix%7D
[A _ _begin_bmatrix_ 1 _ 2 _ 3_ 0_ 5 _6 _ 7_ 0 _9 _end_bmatrix]: https://private.codecogs.com/gif.latex?A%20%3D%20%5Cbegin%7Bbmatrix%7D%201%20%26%202%20%26%203%5C%5C%200%26%205%20%266%20%5C%5C%207%26%200%20%269%20%5Cend%7Bbmatrix%7D