Engineering Analysis/Spectral Decomposition

If &lambda;i 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.