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Is there a general solution to the following matrix equation.

$A - BAB^T = C$
where B is known but can be any non-symmetric square matrix, C is known and invertible, all are n by n matrices. Is there a solution to A? or we need to use numerical methods?

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    At worst it is just system of linear equations with the $n^2$ entries of $A$ as unknowns.2012-09-05

1 Answers 1

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This is a discrete Lyapunov equation, and stable, accurate numerical methods exist to solve it (for certain conditions on $C$).

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    Thank you. Yes, totally agree. The analytical form may help me draw some intuitions but a numerical method (matlab has it) may be more desirable when n is large.2012-09-05