Module extendr_api::prelude::modules::evd

Expand description

Low level implementation of the eigenvalue decomposition of a square diagonalizable matrix.

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.

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  • Indicates whether the eigenvectors are fully computed, partially computed, or skipped.

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