
Re: why the sigma of symmetrical svd for a real symmetric matrix is negative?
Posted:
Dec 27, 2012 7:30 PM


"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

