Re: ? solving linear eqn

From: Cheng Cosine (acosine_at_ms13.url.com.tw)
Date: 11/24/04 

Date: Wed, 24 Nov 2004 10:22:42 -0700

"Cheng Cosine" <acosine@ms13.url.com.tw> wrote in message
news:co0p7n$oap$1@vegh.ks.cc.utah.edu...
>
> Given A*x = b, here x and b are vectors and A is a matrix, square or not.
>
> I saw the following:
>
> 1) given A, b and then solve for b
>
> but how about the following:
>
> 2) given x and b, solve for A?
>

 Someone suggested to extend (2) into more general form that

all A, x, and b are matrix. Then I can easily analysis A*x = b

as what textbook usually taught to do for A*x = b as usual.

But this approach just remind me another linear equation below.

A*x+x*B = C

Here all are matrices. A is m-by-m and B is n-by-n, while both

x and C are m-by-n.

  I read in some linear system books called this as Lyapunov equation,

and some interesting theorems are given. However, I don't see how

to analysize linear problems of this kind. To be more specific, in analyzing

A*x = b, I read ppl use the eigenvector or spectral expansion or more

generally the SVD. Then one can see when the solution exist and unique.

But I don't see any way to do analysis for A*x+x*B = C.

  Any suggestions?

by Cheng Cosine
   Nov/24/2k4 UT

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