Linear Algebra Foundations: Orthogonality, Symmetric Matrices, and SVD

Many modern technologies, from image compression to recommendation systems, rely on advanced linear algebra. Understanding concepts like orthogonality, symmetric matrices, and singular value decomposition (SVD) is crucial for anyone entering data science, computer graphics, or engineering. This text-based course guides you through these essential mathematical frameworks step-by-step. You will transition from basic vector concepts to confidently analyzing multi-dimensional datasets using advanced matrix factorization techniques. What you'll learn: - Understand the core principles of orthogonality, orthogonal projections, and orthonormal bases. - Apply the Gram-Schmidt process to construct orthogonal bases from scratch. - Explore symmetric matrices, their unique properties, and the spectral theorem. - Master Singular Value Decomposition (SVD) and its role in data compression and dimensionality reduction. - Practice solving mathematical problems through detailed, written step-by-step derivations. The course starts with foundational definitions of orthogonality before moving into symmetric matrices and culminating in the powerful SVD framework. Every module features clear written explanations, practical examples, and self-assessment exercises to solidify your mathematical intuition. This course is designed for beginners in linear algebra, aspiring data scientists, and students looking for a clear, written guide to these essential mathematical concepts. Start reading today to unlock the mathematical foundations of modern data science.