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?