Let $S$ and $T$ be two $n \times n$ matrices that have no eigenvalues in common. Show that the transformation $\Phi$ that maps the $n\times n$ matrices, $M_n$, to the $M_n$ and is defined by the formula $\Phi(A):=SA - AT $ is invertible.
2026-04-18 12:57:13.1776517033
Linear Transformation Map with eigenvalues
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