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