Practical Linear Algebra by Gerald Farin

A Geometry Toolbox

This textbook presents linear algebra from a hands-on, geometric and computational perspective, developing core concepts such as vectors, matrices, linear systems, vector spaces, bases and linear transformations alongside determinants, eigenvalues and the singular value decomposition. Emphasis is placed on algorithms and numerical methods (for example Gaussian elimination, QR factorization and least-squares), with many illustrative examples, exercises and implementation-minded discussion. Applications to computer graphics and geometric modeling, including curves and surfaces, are used throughout to build geometric intuition and show how theory translates into practical computations.