Mr. Integral
Math notes/Linear Algebra/Eigenvalues and Dynamics

Diagonalization and Discrete Dynamics — Cheat sheet

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Core rule

A=VDV−1⇒Ak=VDkV−1.A=VDV^{-1}\Rightarrow A^k=VD^kV^{-1}.

Watch for

Diagonalization requires a full independent eigenvector basis. Repeated eigenvalues neither guarantee nor rule it out.