The Subspace of Matrices that are Diagonalized by a Fixed Matrix
Problem 33
Suppose that $S$ is a fixed invertible $3$ by $3$ matrix. This question is about all the matrices $A$ that are diagonalized by $S$, so that $S^{-1}AS$ is diagonal. Show that these matrices $A$ form a subspace of $3$ by $3$ matrix space.
(MIT-Massachusetts Institute of Technology Exam)
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