Fix SVD range

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2023-09-30 20:39:59 +02:00
parent 55fb93cb6b
commit efc92016e4

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@ -49,7 +49,8 @@ where:
$\matr{\Sigma} \in \mathbb{R}^{m \times n}$ is a matrix with $\matr{\Sigma}_{i,j} = 0$ (i.e. diagonal if it was a square matrix) and
the singular values $\sigma_i, i = 1 \dots \min\{m, n\}$ on the diagonal.
By convention $\sigma_1 \geq \sigma_2 \geq \dots \geq \sigma_r \geq 0$.
Note that singular values $\sigma_j = 0$ for $(r + 1) \leq j \leq n$.
Note that singular values $\sigma_j = 0$ for $(r + 1) \leq j \leq \min\{m, n\}$
(i.e. singular values at indexes after $\text{rank}(\matr{A})$ are always 0).
\end{itemize}
\marginnote{Singular value equation}