I was confused by the formula for similar matrices. The book says $A = S^{-1} B S$ if $A$ and $B$ are similar. But I'm wondering if $S B S^{-1}$ makes a difference at all? Which formula should I stick to in general?
2026-03-26 08:14:35.1774512875
Similar Matrices Formula
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$S^{-1}BS=(S^{-1})B(S^{-1})^{-1}$, which is of the form $PBP^{-1}$, so without loss of generality we can assume $S^{-1}BS$.