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Engineering Analysis/Spectral Decomposition

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Engineering Analysis

If λi are are the n distinct eigenvalues of matrix A, and vi are the corresponding n distinct eigenvectors, and if wi are the n distinct left-eigenvectors, then the matrix A can be represented as a sum:

A = \sum_{i = 1}^n \lambda_i v_i w_i^T

this is known as the spectral decomposition of A.

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