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- A is diagonalizable ⇔ it has n linearly independent eigenvectors. Then A = PDP⁻¹: P’s columns are eigenvectors, D’s diagonal the matching eigenvalues. Aᵏ = PDᵏP⁻¹.
Memory trickn distinct eigenvalues ⇒ diagonalizable
(sufficient, not necessary).
Related real-exam questions
🎯 How this can come up · 2 questions
True / False
A 3×3 matrix with 3 distinct eigenvalues is diagonalizable.
True.
True / False
Every diagonalizable matrix is invertible.
False. 0 can be an eigenvalue.
