From: <HIDDEN>
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Subject: Re: Matrix decomposition in vectors
Date: Mon, 26 Jan 2009 17:51:01 +0000 (UTC)
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"Umair Mansoor" <> wrote in message <glkkq2$8i2$>...
> Can someone tell me how can I decompose a matrix in vectors, like, a 2x2 matrix in to the product of a 2x1 and 1x2 vectors?

  To decompose any matrix in the way you propose, use the singular value decomposition function, 'svd'.  If there is only one non-zero singular value, then that gives you a solution.  If there are more than one, no solution is possible.

  If the matrix is A, do

 [U,S,V] = svd(A);

Suppose the only non-zero value in S is S(1,1).  Then you have

 A = U*S*V' = (U(:,1)*S(1,1)) * (V(:,1)')

which gives you a solution and shows you that the choice is only arbitrary up to a multiplicative constant.  Otherwise no solution is possible.

Roger Stafford