Vectors and Spaces

Vectors and Spaces is a complete one-semester course in linear algebra for college students, STEM majors and self-learners. It teaches the subject the way a patient teacher would: start with something concrete, notice the patterns, give them names, and build upward, with geometry tying the ideas together.Ten chapters cover systems of linear equations, matrix algebra, vectors and the geometry of R^n, vector spaces, linear transformations, determinants, eigenvalues and eigenvectors, orthogonality, diagonalization and symmetric matrices, and least squares with applications. Every major idea comes with a worked example that shows the full reasoning.The book includes 460 practice questions with complete step-by-step solutions, two full-length practice exams of 60 questions each, a notation guide and glossary, and a computation quick reference for inverses, determinants, eigenvalues and more.