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Thread Subject:
matrix problem

Subject: matrix problem

From: Frank

Date: 2 Jan, 2013 04:34:10

Message: 1 of 4

Hello,

I have a problem:

max Re{Tr(W^H D W B)}
s.t. W^H W = I

where all the matrices are complex and D is complex diagonal. The unknown is W.
How can I find W?

Thanks a lot.

Frank

Subject: matrix problem

From: Bruno Luong

Date: 2 Jan, 2013 07:53:09

Message: 2 of 4

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <kc0dc2$omi$1@newscl01ah.mathworks.com>...
> Hello,
>
> I have a problem:
>
> max Re{Tr(W^H D W B)}
> s.t. W^H W = I
>
> where all the matrices are complex and D is complex diagonal. The unknown is W.
> How can I find W?
>

As I understand Re{Tr(W^H D W B)} is a *vector* function, what do you mean by maximizing it?

Bruno

Subject: matrix problem

From: Frank

Date: 2 Jan, 2013 08:05:09

Message: 3 of 4

In Re{Tr(W^H D W B)} , Tr means trace and therefore, Re{Tr(W^H D W B)} is a scalar.

Subject: matrix problem

From: Bruno Luong

Date: 2 Jan, 2013 08:18:09

Message: 4 of 4

"Frank " <allinone_2003@yahoo.com.hk> wrote in message <kc0pnl$4pd$1@newscl01ah.mathworks.com>...
> In Re{Tr(W^H D W B)} , Tr means trace and therefore, Re{Tr(W^H D W B)} is a scalar.

OK, Re{Tr(W^H D W B)} is quadratic in W, W^t*W = I is again quadratic constraints.

I think you should checkout of fmincon, or maybe you could transform to QEP by the technique explained here
W. Gander, G. H. Golub, and U. Von Matt, "A constrained eigenvalue problem", Linear Algebra Appl., 114-115 (1989), pp. 815839.

Bruno

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