The bookUnit 1 · Eigenvalues and Canonical Forms24 / 83

Diagonalisability criteria

Why this is asked: Decide diagonalisability from a single equation or property: idempotent, involution, Aᵏ = I, nilpotent, symmetric, normal, distinct eigenvalues. Know over which field.

Diagonalisability — the criteria card

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Is this matrix diagonalisable? The decision procedureinteractive

The criterion that always settles it, and the two conditions that look sufficient but are not.

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Let A be a real n×n matrix. Which of the following imply that A is diagonalisable over $\mathbb{R}$ ?

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