I am looking for a solution (or approximate solution) for the following equations with vectorization. Let $X$ be $m\times n$ matrix of unknown parameters, $A,B$ and $C$ are comfortable matrices (i.e., $A$ be $m\times m$, $B$ be $n\times n$, $C$ be $m\times n$), $vec$ is the vectorization, what's the typical solution of \begin{equation} \ vec\left( AX+XB\right) =vec\left( C\right) \ \end{equation} looks like? Is there anyway to get a solution of $X$ in a simple formula? I am looking for a solution of $vec(X)=?$ Many thanks!
Solution of vectorized equation
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vector-spaces
matrix-equations
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0Can you give the dimensions of the other matrices ? & explain what you mean by vectorised (if needs be) – 2017-02-13
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0Hi, Donald, I edit the question following your suggestions. I am looking for $vec(x)$ or a solution of $X$ from the above vectorized equation. Thanks – 2017-02-13
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0These were the dimensions that I had figured. So we are given $A$,$B$ & $C$ and you want $X$ right ? & it is just normal regular matrix multiplication ? ... should be doable , it is $n*m$ linear equations is as many unknowns. – 2017-02-13
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0Do mind to give me some reference on how to get $X$ or $vec(X)$? Thanks – 2017-02-13