Linear Algebra: Diagonalization and Singular Value Decomposition

Understanding how to break down complex matrices into simpler, interpretable parts is a fundamental skill in data science, physics, and engineering. This text-based course guides you step-by-step through the core mathematical concepts behind matrix diagonalization and Singular Value Decomposition (SVD). You will start with the absolute basics of eigenvalues and eigenvectors, learning the core definitions before moving on to advanced factorization techniques. By the end of this course, you will confidently calculate factorizations, interpret geometric transformations, and understand how these mathematical principles power modern technologies like recommendation systems and image compression. What you'll learn: - Understand the foundational concepts of eigenvalues, eigenvectors, and characteristic equations - Compute the diagonalization of square matrices using step-by-step algebraic methods - Master the mechanics of Singular Value Decomposition for both square and rectangular matrices - Apply geometric interpretations to understand how SVD transforms vector spaces - Explore modern applications of SVD, including principal component analysis and dimensionality reduction - Practice your skills with targeted conceptual exercises and detailed written walkthroughs This course begins with key terminology and foundational linear algebra definitions, ensuring you have a strong grip on the basics before introducing complex factorization algorithms. You will progress through structured readings, clear mathematical proofs, and practical analytical scenarios. This course is designed for beginners, students, and aspiring data professionals who want to build a rock-solid mathematical foundation without needing prior advanced engineering background. Start reading today to unlock the power of matrix factorization.