Includes bibliographical references (p. [473]-474) and index.

Vector Spaces.- Linear Transformations.- The Isomorphism Theorems.- Modules I: Basic Properties.- Modules II: Free and Noetherian Modules.- Modules over a Principal Ideal Domain.- The Structure of a Linear Operator.- Eigenvalues and Eigenvectors.- Real and Complex Inner Product Spaces.- Structure Theory for Normal Operators.- Metric Vector Spaces: The Theory of Bilinear Forms.- Metric Spaces.- Hilbert Spaces.- Tensor Products.- Positive Solutions to Linear Systems: Convexity and Separation.- Affine Geometry.- Operator Factorizations: QR and Singular Value.- The Umbral Calculus.- References.- Index.

This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications.The second edition contains two new chapters: a chapter on convexity, separation and positive solutions to linear systems and a chapter on the QR decomposition, singular values and pseudoinverses. The treatments of tensor products and the umbral calculus have been greatly expanded and there is now a discussion of determinants (in the chapter on tensor products), the complexification of a real vector space, Schur's lemma and Gersgorin disks.