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I have two questions here.

Suppose $A \in \mathbf{C}^{k \times k} $ and $B \in \mathbf{C}^{k \times l}$, I want to solve the equation $$ AT=B $$ to within an accuracy of $\epsilon$. Which numerical method should I use?

If $A$ is ill-conditioned, there is a large set of solutions. How could I pick one for which $\|T\|_F$ is minimized. $\|T\|_F$is Frobenius norm of the matrix

Thanks in advance.

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The singular value decomposition is appropriate here. –  J. M. Nov 10 '11 at 8:57
Thanks for your hint. I'll have a try. –  Yao Jin Nov 12 '11 at 13:40

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