If we let $A$ be an $n$ by $n$ matrix with an eigenvalue of $1$ with multiplicity $n$, is it accurate to say that $A$ is always diagonalizable?
2026-03-27 12:12:45.1774613565
Eigenvalue multiplicity of $n$ by $n$ matrices.
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If $A$ were diagonalizable then your diagonal matrix would be identity matrix $I$ and you would have $A=PIP^{-1} = I$.
So if $A$ is not identity matrix and has $n$ eigenvalues $=1$ then it is not diagonalizable.