The fourth and most recent edition of Linear Algebra Done Right is an Open Access book available in English, Chinese, Farsi, Greek, and Portuguese. Other languages are coming soon.
Electronic versions of this fourth edition, which has a Creative Commons BY-NC license, are legally availble without cost at the links below.
The fourth edition of Linear Algebra Done Right contains over 250 new exercises and over 70 new examples, along with several new topics and multiple improvements throughout the book. See page xvi in the English file linked above for a list of major improvements and additions in the fourth edition.
The hardcover print version of the fourth edition of Linear Algebra Done Right is available from Amazon at the link below.
Print versions of translations of the fourth edition into Greek and into Portuguese are available at booksellers in appropriate countries.
Print versions of translations of the third edition into Basque and Chinese are available from Amazon at the links below.
This best-selling textbook for a second course in linear algebra is aimed at undergraduate 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.
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 then introduced, leading to the finite-dimensional spectral theorem and its consequences such as the singular value decomposition. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. Determinants are cleanly introduced via alternating multilinear forms.