Designed for undergraduate mathematics majors and graduate students, Linear Algebra Done Right presents a second course in linear algebra focused on understanding the structure of linear operators on finite-dimensional vector spaces. It assumes mathematical maturity rather than specific prior knowledge, and gives attention to motivating concepts and developing proofs clearly.

From vector spaces to operators

The progression begins with vector spaces, linear independence, span, bases, and dimension, then moves to linear maps, polynomials, eigenvalues, and eigenvectors. Inner-product spaces lead into the finite-dimensional spectral theorem, while generalized eigenvectors offer another way to examine the structure of operators. Determinants are treated near the end of the book, rather than as the starting point for the subject.

Expanded topics and exercises

The fourth edition gives fuller treatment to the singular value decomposition and its consequences. A new chapter introduces multilinear algebra through bilinear and quadratic forms, tensor products, and determinants approached by alternating multilinear forms. The edition also makes greater use of the minimal polynomial in proofs and adds more than 250 exercises.

A text built for active study

Each section is followed by original exercises at varying levels of difficulty, giving readers opportunities to reinforce and work with the concepts. The eBook is available in open access, and the book is part of the Undergraduate Texts in Mathematics series.