04.MATLAB矩阵处理基础

今天药忘吃喽~ 2023-06-21 15:21 9阅读 0赞

**1.特殊矩阵的建立**

**   单位矩阵**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70][]

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**随机矩阵**

rand产生从0到1之间均匀分布的随机矩阵，randn产生均值为0，方差为1的标准正态分布的随机矩阵

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 2][]

**产生10行1列 0到1之间的随机向量**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 3][]

**产生1行10列服从正态分布的随机向量**

![20191213120027255.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 4][]

![2019121312002328.png][]

![20191213120027266.png][]

**2.矩阵和向量运算**

MATLAB运算以矩阵为单位，可以直接实现矩阵的加法、数乘等运算以及矩阵的行列式、矩阵的秩、矩阵的逆以及转置等运算。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 5][]

![20191213120024224.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 6][]

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![20191213120027311.png][]

**3.线性方程组的求解**

A = \[1, 2, 3; 1, 4, 9; 1 8 27\];  %初始向量

b = \[5, -2, 6\]';  %初始列向量

x = inv(A)\*b %使用A的逆矩阵求解

x = A\\b   %或者直接使用左除运算

**4.矩阵的相似化简和分解**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 8][]

A = \[0 3 3; -1 8 6; 2 -14 -10\];

jordan(A)

\[V J\] = jordan(A)

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 9][]

A = \[1 0 i; 0 2 0; -i 0 1\];

eig(A)

\[E D\] = eig(A)

**5.向量和矩阵的范数**

范数运算，包括1范数，2范数和无穷范数以及f范数，使用norm函数。

%向量和矩阵的范数

A = \[0 3 3; -1 8 6; 2 -14 -10\];

norm(A, 1)

norm(A, 2)

norm(A, inf)

norm(A, 'fro')

**6.矩阵分析**

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 10][]

%函数矩阵

syms x

A = \[sin(x) exp(x) 1; cos(x) x^2 + 1 log(x)\];

diff(A) %求矩阵A的一阶导数

diff(A, 2) %求矩阵A的二阶导数

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L0FuZHk3MTA2NjA1NDE_size_16_color_FFFFFF_t_70 11][]

%计算A的矩阵函数

A = \[0 1; 0 -2\];

expA = funm(A, @exp)

expA = expm(A)

sinA = funm(A, @sin)

cosA = funm(A, @cos)

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[2019121312002328.png]: https://img-blog.csdnimg.cn/2019121312002328.png
[20191213120027266.png]: https://img-blog.csdnimg.cn/20191213120027266.png
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