Eigendecomposition of a matrix

In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix $A$ into a canonical form given by ⁠$A=QDQ^{\mathsf {-1}}$⁠, where $D$ is a diagonal matrix containing the eigenvalues of $A$ on the diagonal, and $Q$ is a matrix whose columns are the corresponding eigenvectors of ⁠$A$⁠. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem.