Engineering Analysis/Spectral Decomposition

< Engineering Analysis

If λ_i are the n distinct eigenvalues of matrix A, and v_i are the corresponding n distinct eigenvectors, and if w_i 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.

This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.