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Thomas Dehaeze 2020-09-21 17:02:44 +02:00
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content/zettels/singular_value_decomposition.md
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@ -45,7 +45,7 @@ We define \\(u\_1 = \bar{u}\\), \\(v\_1 = \bar{v}\\), \\(u\_k=\ubar{u}\\) and \\
## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices} ## SVD to pseudo inverse rectangular matrices {#svd-to-pseudo-inverse-rectangular-matrices}
This is taken from [Preumont's book](preumont18_vibrat_contr_activ_struc_fourt_edition.md). This is taken from [Singular Value Decomposition]({{< relref "preumont18_vibrat_contr_activ_struc_fourt_edition" >}}).
The **Singular Value Decomposition** (SVD) is a generalization of the eigenvalue decomposition of a rectangular matrix: The **Singular Value Decomposition** (SVD) is a generalization of the eigenvalue decomposition of a rectangular matrix:
\\[ J = U \Sigma V^T = \sum\_{i=1}^r \sigma\_i u\_i v\_i^T \\] \\[ J = U \Sigma V^T = \sum\_{i=1}^r \sigma\_i u\_i v\_i^T \\]