inverse of complex matrix

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Ben Marinberg
Ben Marinberg 2020-8-27
评论： Stephen23 2020-8-31
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?
  1 个评论
Stephen23
Stephen23 2020-8-27
"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

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Bruno Luong
Bruno Luong 2020-8-27
编辑：Bruno Luong 2020-8-27
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
>>
  2 个评论
Ben Marinberg
Ben Marinberg 2020-8-31
My matrix didn't had that high of a condition number, also it didn't gave any warning..
Stephen23
Stephen23 2020-8-31
@Ben Marinberg : please save your matrix in a .mat file and upload it by clicking the paperclip button.

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