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---
title: mtx_eig
description: eigenvalue decomposition of a matrix
categories:
- object
pdcategory: Matrix Transformation
see_also:
- mtx_svd
inlets:
1st:
- type: matrix
description: \(n\times n\) matrix \(\boldsymbol A\) to decompose
outlets:
1st:
- type: list
description: list of real parts of the \(n\) eigenvalues \(\boldsymbol \sigma\)
2nd:
- type: list
description: list of imaginary parts of the \(n\) eigenvalues \(\boldsymbol \sigma\)
3:
- type: matrix
description: \(n\times n\) real part of the eigenvector matrix \(\boldsymbol V\)
4:
- type: matrix
description: \(n\times n\) imaginary part of the eigenvector matrix \(\boldsymbol V\)
draft: false
---
This object depends on the GNU Scientific Library. The matrices lists involved have the properties:
$$ \boldsymbol A = \boldsymbol V \operatorname{diag}\lbrace \boldsymbol \sigma\rbrace \boldsymbol V^{-1} $$
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