Matlab中特殊的矩阵函数

1、零空间函数

>> A = [1 2 3 4;5 6 7 8;9 10 11 12;13 14 15 16]

A =

     1     2     3     4
     5     6     7     8
     9    10    11    12
    13    14    15    16

>> null(A)

ans =

    0.2826   -0.4692
   -0.7265    0.4150
    0.6053    0.5776
   -0.1614   -0.5234

2、正交空间函数

>> B = magic(8)

B =

    64     2     3    61    60     6     7    57
     9    55    54    12    13    51    50    16
    17    47    46    20    21    43    42    24
    40    26    27    37    36    30    31    33
    32    34    35    29    28    38    39    25
    41    23    22    44    45    19    18    48
    49    15    14    52    53    11    10    56
     8    58    59     5     4    62    63     1

>> orth(B)

ans =

   -0.3536    0.5401    0.3536
   -0.3536   -0.3858   -0.3536
   -0.3536   -0.2315   -0.3536
   -0.3536    0.0772    0.3536
   -0.3536   -0.0772    0.3536
   -0.3536    0.2315   -0.3536
   -0.3536    0.3858   -0.3536
   -0.3536   -0.5401    0.3536

3、伪逆函数

>> C = magic(6)

C =

    35     1     6    26    19    24
     3    32     7    21    23    25
    31     9     2    22    27    20
     8    28    33    17    10    15
    30     5    34    12    14    16
     4    36    29    13    18    11

>> pinv(C)

ans =

    0.0115   -0.0386    0.0254    0.0054   -0.0139    0.0192
    0.0023   -0.0201    0.0162    0.0146   -0.0324    0.0285
   -0.0081    0.0030   -0.0151    0.0042    0.0277   -0.0027
    0.0540   -0.0417   -0.0016    0.0601   -0.0664    0.0046
   -0.0409    0.0231    0.0285   -0.0533    0.0355    0.0162
   -0.0097    0.0833   -0.0444   -0.0220    0.0586   -0.0568
>> inv(C)
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  1.600321e-18. 

ans =

   1.0e+15 *

   -1.1259   -0.0000    1.1259    1.1259   -0.0000   -1.1259
   -1.1259   -0.0000    1.1259    1.1259   -0.0000   -1.1259
    0.5629    0.0000   -0.5629   -0.5629    0.0000    0.5629
    1.1259    0.0000   -1.1259   -1.1259    0.0000    1.1259
    1.1259    0.0000   -1.1259   -1.1259    0.0000    1.1259
   -0.5629         0    0.5629    0.5629   -0.0000   -0.5629



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