An eigendecomposition $A = P D P^{-1}$, with $D$ diagonal
Definition: eigendecomposition
Terms
| Term | This example | Why |
|---|---|---|
| singular value decomposition | ✗ | An eigendecomposition $A = P D P^{-1}$ is not a singular value decomposition, because the columns of $P$ need not be orthonormal, and the eigenvalues in $D$ can be negative or complex. For a symmetric positive semidefinite matrix, the two decompositions coincide. |
Distinctions using this example
- Types of matrix decompositions: An eigendecomposition is not a singular value decomposition, because $P$ need not be orthogonal, and the entries of $D$ can be negative or complex.