Linear Algebra Done Right

Description

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. Front Matter....Pages i-xvii Vector Spaces....Pages 1-26 Finite-Dimensional Vector Spaces....Pages 27-49 Linear Maps....Pages 51-116 Polynomials....Pages 117-130 Eigenvalues, Eigenvectors, and Invariant Subspaces....Pages 131-161 Inner Product Spaces....Pages 163-202 Operators on Inner Product Spaces....Pages 203-240 Operators on Complex Vector Spaces....Pages 241-274 Operators on Real Vector Spaces....Pages 275-294 Trace and Determinant....Pages 295-331 Back Matter....Pages 333-340