Math — Eigendecomposition
Diagonalisation, matrix powers and the spectral theorem.
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A = PDP^{-1}
A^n = PD^nP^{-1}
\text{symmetric } A: A = Q\Lambda Q^\top
\operatorname{tr}(A) = \sum_i \lambda_i, \quad \det(A) = \prod_i \lambda_i