Let $A, B$ be invertible and simultaneously diagonalizable matrices. I want to conjugate the matrix $B$ by some invertible matrix $P$. It is not always the case that there exists some invertible matrix $Q$ such that $$A P B P^{-1} = Q A B Q^{-1}.$$ Can we characterize the matrices for which there does always exist such a $Q$? Possibly for a fixed $A$?
2026-03-14 11:29:22.1773487762
Conjugating (the product of) simultaneously diagonalizable matrices
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