matlab 矩阵变换

川长思鸟来 2022-04-10 04:09 462阅读 0赞

# matlab 矩阵变换 #

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**对角阵 –diag()  
三角阵----triu(),tril()  
矩阵的转置 —’  
矩阵的旋转 rot90()  
矩阵的翻转 –fliplr() –flipud()  
矩阵求逆 –inv()**

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## 对角阵 –diag() ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mjg3ODc1OA_size_16_color_FFFFFF_t_70]

>> diag(1:5)
    ans =
         1     0     0     0     0
         0     2     0     0     0
         0     0     3     0     0
         0     0     0     4     0
         0     0     0     0     5

## 三角阵----triu(),tril() ##

### 上三角矩阵—triu() ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mjg3ODc1OA_size_16_color_FFFFFF_t_70 1]

### 下三角矩阵–Tril() ###

>> tril(ones(5),1)
    ans =
         1     1     0     0     0
         1     1     1     0     0
         1     1     1     1     0
         1     1     1     1     1
         1     1     1     1     1

## 矩阵的转置 —’ ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mjg3ODc1OA_size_16_color_FFFFFF_t_70 2]  
如果是实数，转置和共轭转置的结果一样

>> A  = [1,3;3+4i,1-2i]
    A =
       1.0000 + 0.0000i   3.0000 + 0.0000i
       3.0000 + 4.0000i   1.0000 - 2.0000i
    >> A'
    ans =
       1.0000 + 0.0000i   3.0000 - 4.0000i
       3.0000 + 0.0000i   1.0000 + 2.0000i
    >> A.'
    ans =
       1.0000 + 0.0000i   3.0000 + 4.0000i
       3.0000 + 0.0000i   1.0000 - 2.0000i

## 矩阵的旋转 rot90() ##

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mjg3ODc1OA_size_16_color_FFFFFF_t_70 3]

### 顺时针旋转90度：rot90(A,-1) ###

## 矩阵的翻转 –fliplr() –flipud() ##

### Fliplr(A)—左右翻转 l-left;r-right ###

### Flipud(A)—上下翻转 u-up;d-down ###

>> A = rand(5)
    A =
        0.3500    0.3517    0.2858    0.0759    0.1299
        0.1966    0.8308    0.7572    0.0540    0.5688
        0.2511    0.5853    0.7537    0.5308    0.4694
        0.6160    0.5497    0.3804    0.7792    0.0119
        0.4733    0.9172    0.5678    0.9340    0.3371
    >> fliplr(A)
    ans =
        0.1299    0.0759    0.2858    0.3517    0.3500
        0.5688    0.0540    0.7572    0.8308    0.1966
        0.4694    0.5308    0.7537    0.5853    0.2511
        0.0119    0.7792    0.3804    0.5497    0.6160
        0.3371    0.9340    0.5678    0.9172    0.4733
    >> flipud(A)
    ans =
        0.4733    0.9172    0.5678    0.9340    0.3371
        0.6160    0.5497    0.3804    0.7792    0.0119
        0.2511    0.5853    0.7537    0.5308    0.4694
        0.1966    0.8308    0.7572    0.0540    0.5688
        0.3500    0.3517    0.2858    0.0759    0.1299

## 矩阵求逆 –inv() ##

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mjg3ODc1OA_size_16_color_FFFFFF_t_70 4][]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mjg3ODc1OA_size_16_color_FFFFFF_t_70 5]

>> A = [1,2,3;1,4,9;1,8,27]
    A =
         1     2     3
         1     4     9
         1     8    27
    >> b = [5,-2,6]
    b =
         5    -2     6
    >> x = inv(A)*b'
    x =
       23.0000
      -14.5000
    3.6667

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