Introduction To Linear Algebra by Gilbert Strang

This textbook introduces fundamental concepts of linear algebra through a blend of geometric intuition and computational methods, covering vectors and matrices, systems of linear equations, linear independence, bases and subspaces, rank and determinants, eigenvalues and eigenvectors, and orthogonality. It emphasizes practical solution techniques such as Gaussian elimination, QR factorization and the singular value decomposition, and presents applications to least squares problems, differential equations and data analysis. The exposition balances theory, proofs and numerous examples to develop both conceptual understanding and algorithmic skill for use in engineering, science and applied mathematics.