Date: Dec 26, 2012 9:25 PM
Author: Rick
Subject: why the sigma of symmetrical svd for a real symmetric matrix is negative?

  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