From efc92016e4cf523be0399b5424feb2cac5c93999 Mon Sep 17 00:00:00 2001
From: NotXia <35894453+NotXia@users.noreply.github.com>
Date: Sat, 30 Sep 2023 20:39:59 +0200
Subject: [PATCH] Fix SVD range

---
 .../sections/_matrix_decomp.tex                                | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/statistical-and-mathematical-methods-for-ai/sections/_matrix_decomp.tex b/src/statistical-and-mathematical-methods-for-ai/sections/_matrix_decomp.tex
index bb677db..1723808 100644
--- a/src/statistical-and-mathematical-methods-for-ai/sections/_matrix_decomp.tex
+++ b/src/statistical-and-mathematical-methods-for-ai/sections/_matrix_decomp.tex
@@ -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}