# Engineering Analysis/Spectral Decomposition

If λi 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:

${\displaystyle A=\sum _{i=1}^{n}\lambda _{i}v_{i}w_{i}^{T}}$

this is known as the spectral decomposition of A.