matlab 矩阵变换

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()

>> 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()

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 —’

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()

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()

>> 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