Add SMM backpropagation

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

@@ -259,8 +259,8 @@ it is possible to use the basis of $U$.\\
 Let $m = \text{dim}(U)$ be the dimension of $U$ and 
 $\matr{B} = (\vec{b}_1, \dots, \vec{b}_m) \in \mathbb{R}^{n \times m}$ an ordered basis of $U$.
 A projection $\pi_U(\vec{x})$ represents $\vec{x}$ as a linear combination of the basis:
-\[ \pi_U(\vec{x}) = \sum_{i=1}^{m} \lambda_i \vec{b}_i = \matr{B}\vec{\lambda} \]
-where $\vec{\lambda} = (\lambda_1, \dots, \lambda_m)^T \in \mathbb{R}^{m}$ are the new coordinates of $\vec{x}$ 
+\[ \pi_U(\vec{x}) = \sum_{i=1}^{m} \lambda_i \vec{b}_i = \matr{B}\vec{\uplambda} \]
+where $\vec{\uplambda} = (\lambda_1, \dots, \lambda_m)^T \in \mathbb{R}^{m}$ are the new coordinates of $\vec{x}$ 
 and is found by minimizing the distance between $\pi_U(\vec{x})$ and $\vec{x}$.