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Topic: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Replies: 4   Last Post: Dec 27, 2012 7:30 PM

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Greg Heath

Posts: 5,976
Registered: 12/7/04
Re: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Posted: Dec 27, 2012 7:30 PM
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"Rick" wrote in message <kbgbi5$g5n$1@newscl01ah.mathworks.com>...
> Hi everyone,
> as we know, for a real symmetric matrix A, A, there exists a singular value decomposition as A=USU', and S should be a rectangular diagonal matrix with nonnegative real numbers on the diagonal. But when I use the command schur(),
> it seems that S appears negative real numbers on the diagonal as the following. Is there any problem?
>
> Thanks a lots!
>
>

> >>A=
> -1.3410 0.5350 0.2995 -1.1138
> 0.5350 -2.5191 -0.1422 0.4953
> 0.2995 -0.1422 -1.4695 0.2981
> -1.1138 0.4953 0.2981 -2.2897
>

> >>[u,s]=schur(A)
>
> u =
>
> -0.4768 -0.2191 0.0448 0.8501
> 0.5549 -0.8260 0.0177 0.0974
> 0.1944 0.1630 0.9621 0.1004
> -0.6534 -0.4931 0.2685 -0.5078
>
>
> s =
>
> -3.6119 0 0 0
> 0 -2.0534 0 0
> 0 0 -1.3749 0
> 0 0 0 -0.5790


Read the documentation

help schur

doc schur

The schur deconposition yields eigenvalues, not singular values

>> eig(A)

ans =

-3.6119
-2.0534
-1.375
-0.57902

>> svd(A)

ans =

3.6119
2.0534
1.375
0.57902

Hope this helps

Greg



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