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The eigenvalue decomposition of a square matrix $M$ of shape $(n, n)$ is a decomposition into two components $U$, $S$:
- $U$ has shape $(n, n)$ and is invertible,
- $S$ has shape $(n, n)$ and is a diagonal matrix,
- and finally:
$$M = U S U^{-1}.$$
If $M$ is hermitian, then $U$ can be made unitary ($U^{-1} = U^H$), and $S$ is real valued.
Structs§
Enums§
- Compute
Vectors - Indicates whether the eigenvectors are fully computed, partially computed, or skipped.
Functions§
- compute_
evd_ complex - Computes the eigenvalue decomposition of a square complex
matrix. - compute_
evd_ complex_ custom_ epsilon - See
compute_evd_complex. - compute_
evd_ real - Computes the eigenvalue decomposition of a square real
matrix. - compute_
evd_ real_ custom_ epsilon - See
compute_evd_real. - compute_
evd_ req - Computes the size and alignment of required workspace for performing an eigenvalue decomposition. The eigenvectors may be optionally computed.
- compute_
hermitian_ evd - Computes the eigenvalue decomposition of a square hermitian
matrix. Only the lower triangular half of the matrix is accessed. - compute_
hermitian_ evd_ custom_ epsilon - See
compute_hermitian_evd. - compute_
hermitian_ evd_ req - Computes the size and alignment of required workspace for performing a hermitian eigenvalue decomposition. The eigenvectors may be optionally computed.