
Re: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Posted:
Dec 26, 2012 9:59 PM


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

