Update _matrix_decomp.tex

src/year1/statistical-and-mathematical-methods-for-ai/sections/_matrix_decomp.tex

@@ -116,7 +116,7 @@ we can construct a rank-1 matrix (dyad) $\matr{A}_i \in \mathbb{R}^{m \times n}$
 where $\vec{u}_i \in \mathbb{R}^m$ is the $i$-th column of $\matr{U}$ and
 $\vec{v}_i \in \mathbb{R}^n$ is the $i$-th column of $\matr{V}$.
 Then, we can compose $\matr{A}$ as a sum of dyads:
-\[ \matr{A}_i = \sum_{i=1}^{r} \sigma_i \vec{u}_i \vec{v}_i^T = \sum_{i=1}^{r} \sigma_i \matr{A}_i \]
+\[ \matr{A} = \sum_{i=1}^{r} \sigma_i \vec{u}_i \vec{v}_i^T = \sum_{i=1}^{r} \sigma_i \matr{A}_i \]
 
 \marginnote{Rank-$k$ approximation}
 By considering only the first $k < r$ singular values, we can obtain a rank-$k$ approximation of $\matr{A}$: