Linear Algebra

This chapter provides an essential introduction to linear algebra, tailored to improve understanding of its importance in machine learning. It begins by elucidating the fundamental concepts of vectors and matrices, essential building blocks, and delves into their various operations such as addition, subtraction, multiplication, and more advanced procedures such as dot and cross products. The discussion then extends to the critical notions of eigenvectors and eigenvalues, highlighting their significance in matrix analysis and optimisation problems prevalent in machine learning. Central to the chapter is the exploration of Principal Component Analysis (PCA), a key technique in dimensionality reduction, which uses eigenvectors and eigenvalues for dimensionality reduction. The chapter emphasises the practical application of these linear algebraic concepts in deep learning, illustrating their indispensability in algorithm design and model optimisation.