Linear Algebra And Its Applications by Gilbert Strang

This textbook develops the fundamentals of linear algebra with a focus on geometric intuition, computational techniques, and real-world applications: vectors, matrices, solutions of linear systems, matrix factorizations, determinants, eigenvalues and eigenvectors, and the singular value decomposition. It balances theory and practice by explaining why concepts work, demonstrating algorithms for computation, and illustrating uses in engineering, data analysis, differential equations, and computer graphics, while providing numerous examples and exercises to build both conceptual understanding and problem-solving skills.