Introduction to Linear Algebra

Introduction to Linear Algebra stresses finite dimensional vector spaces and linear transformations. Intended for undergraduate majors in mathematics, applied mathematics, chemistry, and physics, the treatment's only prerequisite is a first course in calculus. Proofs are given in detail, and carefully chosen problems demonstrate the variety of situations in which these concepts arise.
After a brief Introduction, the text advances to chapters on the plane, linear dependence, span, dimension, bases, and subspaces. Subsequent chapters explore linear transformations, the dual space in terms of multilinear forms and determinants, a traditional treatment of determinants, and inner product spaces. Extensive Appendixes cover equations and identities; variables, quantifiers, and unknowns; sets; proofs; indices and summations; and functions.

Frank M. Stewart (1917–2011) was Professor of Mathematics at Brown University, where he taught from 1947 until his retirement in 1988.

Preface
Note to the Reader
I. Introduction
II. The Plane
III. Linear Dependence, Span, Dimension, Bases, Subspaces
IV. Linear Transformations
V. The Dual Space: Multilinear Forms, Determinants
VI. Determinants: A Traditional Treatment
VII. Inner Product Spaces
Appendix A. Equations and Identities
Appendix B. Variables and Quantifiers, Unknowns
Appendic C. Sets
Appendix D. Proofs
Appendix E. Indices and Summations
Appendix F. Functions
Index of Symbols
Index
Index of Definitions, Theorems, Corollaries, and Lemmas