Warning: Matrix is close to singular or badly scaled. Results may be inaccurate.

Hello everyone. I have a matrix that is:

0.004648380836025 0.002524412954424 -0.002524412954424 -0.000821180565226 0 0.002524412954424

-0.000626542578981 -0.001620906917604 0.001620906917604 0.002885422409162 0 -0.001620906917604

0.001282496896793 0.002524412954424 -0.002524412954424 0.000861761404389 0 0

0.001534666644492 -0.001620906917604 0.001620906917604 0.001804817797426 0 0

0 -0.002524412954424 0 0.001682941969616 0.002103677462020 -0.002524412954424

0 0.001620906917604 0 -0.001080604611736 -0.001350755764670 0.001620906917604

When i use inv command and take the inverse of this matrix Matlab gives this error:

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 6.491115e-18.

And calculate as:

1.0e+18 *

0.527794489188861 0.821991214493020 -0.527794489188860 -0.821991214493019 -0.187357017765717 -0.291791266736634

0.546782553495766 0.851563372520838 -0.546782553495766 -0.851563372520838 2.167585396954012 3.375814241065342

0.634748301693909 0.988561908269674 -0.634748301693909 -0.988561908269674 2.136359227326393 3.327182363275903

-0.527794489188861 -0.821991214493020 0.527794489188861 0.821991214493020 0.187357017765717 0.291791266736634

-0.188332118507258 -0.293309896163827 0.188332118507258 0.293309896163826 2.900873704769964 4.517843116057024

-1.055588978377721 -1.643982428986040 1.055588978377721 1.643982428986039 0.374714035531435 0.583582533473268

When i write this matrix in a inverse matrix calculator, it gives solutions as:

99.1851027125306 -154.47164513524 -8.121274793333 4.80129825 0 0

0 -0.00000000000000002 0 -0.00000000000000001 -198.0658509629958424 -308.46928628023403707

16.5308504520 -25.7452741 -304.53443810 193.8958581 -198.0658 -308.46928628023403707

99.1851027125 154.471645 280.40804319741965166 129.260218 0 0

317.39232868 246.01702263966 -461.646908 -475.46055895 237.679 -370.163

198.3702054 307.99528228 -197.76706 -310.0436 0 0

I write the solutions badly, however i think it is understandable.

Why Matlab gives this error and calculates wrong? I didn't find any solutions to this.

Thanks for helps.

Answer 1

[Bruno Luong]

It's a warning (not really error)

It means your matrix is numerically not invertible (or almost not invertible)

[Mustafa Duran]

I took its inverse at inverse matrix calculator app and it takes its inverse clearly. I showed it above.

[Bruno Luong]

Sorry but the bunch of numbers do not speak to me, at least not as clear as you are.

[Mustafa Duran]

Thanks, i found the problem. Matlab don't find inverse of matrix clearly if determinant of matrix is near to zero. I am calculated the determinant of it, and gives number like 10^(-47), so i must the write a new code to find inverse of matrix because of Matlab find inverse with the help of determinant.

[Torsten]

... because of Matlab find inverse with the help of determinant.

I can assure you that this is not the case.

From the MATLAB documentation of inv:

inv performs an LU decomposition of the input matrix (or an LDL decomposition if the input matrix is Hermitian). It then uses the results to form a linear system whose solution is the matrix inverse inv(X). For sparse inputs, inv(X) creates a sparse identity matrix and uses backslash, X\speye(size(X)).

[Bruno Luong]

No, MATLAB find inverse by QR factorization. Never with determinant.