MATLAB: Inverse of complex matrix

complex matrixMATLABmatrix inverse

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?

Best Answer

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
>>

Related Solutions

MATLAB: Combining Matrices

e.g.:

>> Ut = triu(randi(45,6))
Ut =
    32     7     5     4     9    25
     0    38    44    18    12     7
     0     0     1    12     7    39
     0     0     0    37     7    28
     0     0     0     0    40    16
     0     0     0     0     0    24
>> Lt = tril(randi(45,6))
Lt =
    19     0     0     0     0     0
     4     3     0     0     0     0
    11    41    17     0     0     0
     6    43     6     6     0     0
     9    23    36    43    37     0
    11    23    18    44     1    21
>> out1 = Ut + tril(Lt,-1)
out1 =
    32     7     5     4     9    25
     4    38    44    18    12     7
    11    41     1    12     7    39
     6    43     6    37     7    28
     9    23    36    43    40    16
    11    23    18    44     1    24
>> % OR
>> out2 = triu(Ut,1) + Lt
out2 =
    19     7     5     4     9    25
     4     3    44    18    12     7
    11    41    17    12     7    39
     6    43     6     6     7    28
     9    23    36    43    37    16
    11    23    18    44     1    21
>>

MATLAB: MATLAB Coder problem with discrete wavelet thresholding

I have finally solved the problem. I've replaced wdencmp with wthcoef and the compiler liked it. Still I have no clue why I got the error, since wdencmp uses wthcoef. Oh well... I am posting the working function if someone needs it.

function out = denoise(input)
    %the thresholding values
    thr =  [...
    0.013347585482866 ; ...
    0.015872023591907 ; ...
    0.144506458583803 ; ...
    0.374411347716711 ; ...
    0.000000000000000 ; ...
    0.000000000000000 ; ...
    0.000000000000000 ; ...
    0.000000000000000 ; ...
    0.000000000000000 ; ...
    0.000000000000000 ; ...
    0.000000000000000 ; ...
    0.000000000000000   ...
    ];
      c = zeros(4170,1); 
      l = zeros(14,1);
      % the deconstruction
      [c,l] = wavedec(input,12,'sym4');
      % thresholding algorithm
      % 1. remove the average value
      c(1:l(1)) = zeros(1,l(1));
      % apply Heuristic SURE to the detail value
      cxc = wthcoef('t',c,l,1:12,thr,'s');
      % the reconstruction
      lxc = l;   
      out = waverec(cxc,lxc,'sym4');
end

Best Answer

Related Solutions

MATLAB: Combining Matrices

MATLAB: MATLAB Coder problem with discrete wavelet thresholding

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