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Find X, and equation $$X^{-1} B X = C$$ where A, B are known square matrices.

And how to find a "best-fit"(least square) X in $$X^{-1} B_i X = C_i$$ Given know pairs of square matrices $\{(A_i,B_i)\},{i=1,2,3...}$

Another (maybe)relevant problem is to find X,Y in $$X B_i Y = C_i$$ Given know pairs $\{(A_i,B_i)\}, i=1,2,3...$

Such problems has came to me several times.

Are there general methods to solve equations where one known matrix is being embedded in two unknown matrices?

somebody4
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  • Your matrix equation is equivalent to $BX = XC$, and here are some hints in the case of $3×3$ matrices: https://math.stackexchange.com/questions/206623/solution-to-ax-xb-for-3-times3-rotation-matrices – Anton Vrdoljak Feb 23 '20 at 08:37
  • wow, thanks, turns out the keyword is "Sylvester equation" – somebody4 Feb 23 '20 at 08:51

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