I have a matrix ${M_k}$ and it has been decomposed such that, ${M_k}={U_k}^{-1}{M_0}{U_k}$. Then it has made equal to, ${M_k}={U_1}^{-k}{M_0}{U_1}^k$. I need to know what matrix operation has been done to obtain this relationship. $U_1$ is a 2 by 2 diagonal matrix and ${M_0}$ is a 2 by 2 matrix. k spans from 0 to $m-1$.
2026-05-05 20:24:01.1778012641
Matrix decomposition and transformation to a different form
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