Linear Algebra and It’s Application in AI Algorithms

Linear algebra forms the mathematical backbone of modern artificial intelligence, providing the essential structures used to represent, transform, and compute data efficiently. This work introduces vectors, vector spaces, and matrices as foundational tools for modeling multidimensional information, connecting systems of linear equations to real AI problem solving. Concepts such as linear transformations, eigenvalues, eigenvectors, orthogonality, and projections are explained with practical relevance to machine learning, neural networks, and feature extraction. Matrix decompositions, including Singular Value Decomposition and eigen analysis, are linked to dimensionality reduction and data compression techniques like Principal Component Analysis. The text demonstrates how matrix operations drive neural computations, optimization processes, and scalable algorithm design, while addressing numerical stability, sparse representations, and computational efficiency.