Non-Trivial Jordan Matrix is not Diagonalizable

Theorem

Let $\mathbf J$ be a Jordan matrix of order $n$, where $n > 1$.

Then $\mathbf J$ is not diagonalizable.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Jordan matrix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Jordan matrix