Linear Algebra Foundations for Science and Data Analysis

Linear algebra is the mathematical backbone of modern engineering, physical sciences, and data analysis. Understanding how vectors and matrices interact allows you to solve complex systems of equations and unlock advanced computational concepts. This text-based course guides you from fundamental definitions to key applications in mathematical sciences. You will develop a strong intuitive and analytical understanding of linear systems, enabling you to apply these concepts to academic exams, data science algorithms, or engineering problems. What you'll learn: Understand core concepts of vector spaces, subspaces, and linear independence; Solve systems of linear equations using Gaussian elimination and matrix operations; Master determinants, eigenvalues, and eigenvectors for system analysis; Explore linear transformations and their representation as matrices; Apply orthogonalization and symmetric matrices to modern data problems; Practice solving theoretical and computational exercises through step-by-step written proofs. You will start with basic definitions of vectors and matrices, gradually moving through system solutions, vector spaces, and eigenvalues. Each chapter pairs clear theoretical explanations with detailed written walkthroughs to build your mathematical confidence. This course is designed for beginners, university students, and aspiring data professionals looking for a clean, structured introduction to the topic. No prior advanced math background is required. Start reading today to build a rock-solid foundation in linear algebra.