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Update exp-svd.md
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morea/nlp/exp-svd.md

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@@ -56,10 +56,13 @@ Multiplying the left equation by \\(X\\) on the left and noting
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$$XV = U\begin{bmatrix} \Lambda \\ {\bf 0}_{(n-p)\times p}\end{bmatrix},$$
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we have
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we have (show why?)
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$$ XX^T X = U \begin{bmatrix} \Lambda^2 \\ {\bf 0}_{(n-p)\times p} \end{bmatrix} V^T, $$
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and therefore noting that \\(V^T = V^{-1}\\), we have
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$$ X = U \begin{bmatrix} \Lambda \\ {\bf 0}_{(n-p)\times p} \end{bmatrix} V^T. $$
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This is the singular value decomposition.
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