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March 27th, 2008, 03:05 AM   #1
pxb
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"Simple" set of linear equations

Hi all, consider an equation AX+XB=C with A,B,C being some known square matrices and X is unknown matrix. This is nothing but a simple set of linear euations for uknowns X_{i,j} and as such it can be easily solved. Problem is that the matrix of this system (for the vector of unknowns X_{i,j}) is quite complicated. I wonder whether there is some elegant closed form form the solution X in terms of A, B, C (i.e. products, inverses, determinants, traces and so on)... ?
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