Linear Algebra: Determinants and Eigenvalues

Many advanced technical fields, from machine learning to computer graphics, rely heavily on the foundational principles of linear algebra. Understanding how matrices scale space and find invariant directions is essential for solving complex real-world computational problems. This text-only course guides you through the core concepts of determinants, eigenvalues, and eigenvectors. You will transition from performing basic matrix operations to understanding the geometric meaning behind these transformations and how they are applied in modern algorithms. What you'll learn: Understand the fundamental definitions and geometric interpretations of determinants; Calculate determinants using cofactor expansion and row reduction techniques; Define and find eigenvalues and eigenvectors for various square matrices; Apply diagonalization to simplify complex matrix power computations; Explore modern applications of eigenvectors, such as search engine ranking and dimensionality reduction. The course begins with foundational definitions and key terminology before guiding you through step-by-step mathematical explanations and practical written exercises. You will progress from basic calculations to conceptual applications in modern technology. Designed for students, aspiring data scientists, and programmers who want to build a strong mathematical foundation, this course requires no advanced prior knowledge of linear algebra. Start reading today to master the mathematical core of modern computing.