Expand description
Symmetric eigenvalue decomposition.
Computes A = Q * Λ * Q^T for a real symmetric matrix A, where:
- Q is an orthogonal matrix whose columns are eigenvectors
- Λ is a diagonal matrix of eigenvalues in ascending order
The algorithm proceeds in two stages:
- Tridiagonalization: Reduce A to tridiagonal form T via blocked Householder
reflections:
A = Q_1 * T * Q_1^T. - Tridiagonal QR iteration: Apply implicit-shift QR iteration to T to compute eigenvalues (and optionally eigenvectors).
- Back-transformation: If eigenvectors are requested, accumulate the
Householder reflections and QR rotations:
Q = Q_1 * Q_2.
Enums§
- EigJob
- Controls what to compute in the eigendecomposition.
Functions§
- syevd
- Computes eigenvalues (and optionally eigenvectors) of a symmetric matrix.