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eigen - Eigenvalues The eigenvalue problem is Ax = x...

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Eigenvalues The eigenvalue problem is Ax = λ x Eigenvalues can be calculated from det { A - λ I } = 0. Note that det { A } = λ 1 λ 2 · · · λ n , Tr { A } = λ 1 + λ 2 + · · · + λ n Power Method for Eigenvalues Start with any x and expand x = c 1 x 1 + c 2 x 2 + · · · + c n x n in terms of the eigenvectors of A (assuming a complete set of eigenvectors), where Ax i = λ i x i . Then applying A to x ( k times), we get as k → ∞ A k x = c 1 λ k 1 x 1 + c 2 λ k 2 x 2 + · · · + c n λ k n x n c j λ k j x j v where | λ j | is the largest eigenvalue in magnitude. We extract the value for
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