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Re: why the sigma of symmetrical svd for a real symmetric matrix
is negative?
Posted:
Dec 26, 2012 9:59 PM
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On 12/26/2012 8:25 PM, Rick wrote:
> 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
>
Just wanted to say that the result by Matlab matches
that of Mathematica.
mat = {{-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}}
Chop@SchurDecomposition[mat][[2]]
{{-3.61188, 0, 0, 0},
{0, -0.579018, 0, 0},
{0, 0, -2.05345, 0},
{0, 0, 0, -1.37496}}
(order is just different, but values the same)
--Nasser
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