Eigendecomposition of a matrix

In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix ${\displaystyle A}$ into a canonical form given by ⁠${\displaystyle A=VDV^{\mathsf {T}}}$⁠, where ${\displaystyle D}$ is a diagonal matrix containing the eigenvalues of ${\displaystyle A}$ on the diagonal, and ${\displaystyle V}$ is an orthogonal matrix whose columns are the corresponding eigenvectors of ⁠${\displaystyle A}$⁠. 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.