## TL;DR

Linear algebra is the mathematics of vectors and matrices, fundamental to computer graphics, machine learning (neural networks), physics simulation, and data science. Core concepts: vectors, matrices, linear transformations, determinants, eigenvalues/eigenvectors, linear systems.

## Core Explanation

Matrix multiplication: AB = C where C_ij = Σ A_ik * B_kj. Neural networks: forward pass is matrix multiplications with activation functions. Gradient descent: derivative of loss w.r.t. weights computed via backpropagation (chain rule on matrices). SVD (Singular Value Decomposition): A = UΣV^T — fundamental to PCA, recommendation systems, image compression.

## Further Reading

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