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[MUG]Svd for complex matrix
| [MUG]Svd for complex matrix |
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Author: Yaxun Liu
Posted: 29/03/2000 06:37:29 GDT
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>> From: "Yaxun Liu"
It seems Maple V5 does not support Svd for complex matrix.
When I use evalf(Svd(A)) on a complex matrix A, e.g.
[1+I 0]
[0 1]
it complains that A contains symbols.
Does any one know how to do a complex svd with Maple V5?
Thanks a lot.
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| [MUG] Re: Svd for complex matrix |
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Author: Maple Group
Posted: 31/03/2000 22:22:44 GDT
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Subject: [MUG]Svd for complex matrix
I may recommend you my symbolic program for computing the svd of any
matrix. You may download it from
http://www.matesco.unican.es/~olazabal/software/maples/algelin/english
Also, you can see a simple example of a maple worksheet in
http://www.matesco.unican.es/~olazabal/software/maples/algelin/english/Metri
cs/cholesky/cholesky23.html
Once you have loaded the whole program (the 5 files!) you may try the following:
> A:= matrix(2,2,[1+I,0,0,1]):
> l:=SVD(A):
> U:=l[1];
U := matrix([[(1/2+1/2*I)*sqrt(2), 0], [0, 1]])
> DD:=l[2];
DD:=matrix([[sqrt(2), 0], [0, 1]])
> V:=l[3];
V:= matrix([[1, 0], [0, 1]])]
> equal(A,evalm(U&*DD&*V));
true
Yours sincerely,
J.M. de Olazabal
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| [MUG] Re: Svd for complex matrix |
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Author: Denis Sevee
Posted: 03/04/2000 19:07:26 GDT
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>> From: Denis Sevee
> On Tue, 28 Mar 2000, Yaxun Liu wrote:
>
> > It seems Maple V5 does not support Svd for complex matrix.
> > Does any one know how to do a complex svd with Maple V5?
If the matrix is not too large and efficiency is not a big problem
you can work through the steps to find the SVD. That is, given
complex matrix A
(1) Compute htranspose(A)&* A
(2) Find the eigenvalues of htranspose(A)&*A. The square roots of these
will be the
singular values.
(3) The (normalized) eigenvectors will be the columns of V.
(4) The normalized columns of AV will be the columns of U. You will
have to add more orthonormal columns if you want U to be square.
denis sevee
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