Suppose I have a $n$ x $n$ matrix M that has only an eigenvalue of 0, and is therefore not invertible. If it is known that this matrix is diagonalisable, how would I prove that M must be a zero matrix?
2026-04-07 06:32:36.1775543556
Proving that a diagonalisable and non-invertible matrix must be a zero matrix
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Let $M = S^{-1}DS$ be a diagonalization, so that $D$ is a diagonal matrix. If $0$ is the only eigenvalue of $M$, what values can be on the diagonal of $D$?