inverse of complex matrix

I'm trying to invert a complex matrix using inv() function.

turns out A*inv(A)≠I and inv(A)*A≠I .

Of course I'm aware of precision errors, but here I got elements greater than 100 off the main diagonal.

Is there any reason for that?

[Stephen23]

"Is there any reason for that?"

Matrix inversion is inhernently numeric unstable. It is also seldom required:

https://www.mathworks.com/help/matlab/ref/inv.html#bu8tv8c-6

Answer 1

[Bruno Luong]

Yes if you have badly conditioned (or badly scaled), or practically singular matrix. Usualy you get a warning message when computing the inverse.

This happens with real matrix as well, such as

>> M=magic(6)

M =

    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

>> iM=inv(M)
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  8.001607e-19. 
 

iM =

   1.0e+15 *

   2.251799813685250  -0.000000000000000  -2.251799813685250  -2.251799813685250  -0.000000000000000   2.251799813685250
   2.251799813685250  -0.000000000000000  -2.251799813685250  -2.251799813685250  -0.000000000000000   2.251799813685250
  -1.125899906842625   0.000000000000000   1.125899906842625   1.125899906842625   0.000000000000000  -1.125899906842625
  -2.251799813685250   0.000000000000000   2.251799813685250   2.251799813685250   0.000000000000000  -2.251799813685250
  -2.251799813685250   0.000000000000000   2.251799813685250   2.251799813685250   0.000000000000000  -2.251799813685250
   1.125899906842624                   0  -1.125899906842624  -1.125899906842624                   0   1.125899906842624

>> M*iM

ans =

  -8.000000000000000                   0   8.000000000000000   8.000000000000000  -1.125000000000000                   0
                   0   1.000000000000000                   0                   0  -0.962843041164940   0.500000000000000
   8.000000000000000  -0.000000000000001  -8.000000000000000  -8.000000000000000  -1.773627835340241   8.000000000000000
   8.000000000000000                   0  -8.000000000000000  -8.000000000000000   0.249352422290674  12.000000000000000
   4.000000000000000   0.000000000000000  -4.000000000000000  -4.000000000000000   0.411509381125735  12.000000000000000
   8.000000000000000                   0  -8.000000000000000  -8.000000000000000  -0.399275413049567  20.000000000000000

>> iM*M

ans =

     0    16     9    -2     4    -2
     0    20     9    -2     4     0
     4    -2    -2    -1     2     1
     2     8     6     0     8     6
     0    -4    -9    -2     0     0
     0     0     0     0     0     0

>> cond(M)

ans =

     4.700154791029550e+16

>> 

[Ben Marinberg]

My matrix didn't had that high of a condition number, also it didn't gave any warning..

[Stephen23]

@Ben Marinberg : please save your matrix in a .mat file and upload it by clicking the paperclip button.