In the mathematical discipline of linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way.
A square (n×n) matrix A can be factorized as
where Q is the square (n×n) matrix whose ith column is the eigenvector qi of A and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, i.e., Λii = λi. Note that only diagonalizable matrices can be factorized in this way.
