Sheldon Axler Writes:
I am happy to announce publication of the fourth edition of Linear Algebra Done Right as an Open Access book. The electronic version of this new fourth edition with a Creative Commons BY-NC license is availble without cost at the link below.
The print version of the new fourth edition of Linear Algebra Done Right is now available from Amazon and from Springer at the links below.
- Amazon: print version of Linear Algebra Done Right, fourth edition
- Springer: print version of Linear Algebra Done Right, fourth edition
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 file linked above for a list of major improvements and additions in the fourth edition.
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.
Matthew Adams (@ythos@dotnet.social) recommends:
If you are interested in #ML and want to get a handle on some foundational #maths, you can do a lot worse than Linear #Algebra Done Right. I have the print version of the 3rd edition, and the 4th edition is available as a PDF as well as in print. https://linear.axler.net/