Linear Algebra Fundamentals: Vectors, Matrices, and Systems

Linear algebra powers the mathematical foundation behind data science, modern computing, engineering, and quantitative sciences. This course provides a structured, accessible approach to understanding vectors, matrices, and linear transformations through clear written explanations and worked mathematical examples. What you'll learn: - Understand core definitions, vector notation, and foundational properties of linear systems. - Solve systems of linear equations using Gaussian elimination and row reduction techniques. - Perform matrix operations, including multiplication, inversion, transpositions, and determinants. - Explore vector spaces, subspaces, linear independence, and basis dimensions. - Understand eigenvalues and eigenvectors and their role in modern data analysis and machine learning. - Apply linear transformation principles to geometric and computational problems. The course begins with foundational vocabulary and elementary vector arithmetic before guiding you methodically through multi-variable matrices and higher-dimensional concepts. Designed entirely for beginners and self-directed learners, no advanced mathematics background is required beyond basic high-school algebra. Begin reading to develop a rigorous and practical grasp of linear algebra.