Introduction to Linear Algebra

This book is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and other more conceptual.

This book is a short text in linear algebra, intended for a one-term course. Lang discusses the relation between the geometry and the algebra underlying the subject, and includes sections on linear equations, matrices and Gaussian elimination, and vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and others are conceptual.

I Vectors. - II Matrices and Linear Equations. - III Vector Spaces. - IV Linear Mappings. - V Composition and Inverse Mappings. - VI Scalar Products and Orthogonality. - VII Determinants. - VIII Eigenvectors and Eigenvalues. - Answers to Exercises.