This course aims to equip students with the necessary knowledge and techniques in linear algebra to enable them to study linear least squares optimization and machine learning. Topics include vector and matrix operations, linear systems, matrix inverse, decomposition, eigendecomposition, and singular value decomposition. These techniques will be applied to topics including regression, classification, model validation, inversion, regularization, constrained least squares problem, clustering, and dimensionality reduction. Numerical computation is used throughout the course as a learning tool. No previous knowledge of linear algebra is assumed.