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 or page xi in the Chinese file linked above for a list of major improvements and additions in the fourth edition.
Linear Algebra Done Right Solutions Axler. S. (2024) Linear Algebra Done Right. 4th edn.
The exposition presents a rigorous treatment of linear algebra with an emphasis on abstract vector spaces and the structure of linear maps and with few applications. The “Done Right” in the title refers to the author’s decision to develop the theory of eigenvalues and eigenvectors without using determinants.
The audacious title of this book deserves an explanation. Almost all linear algebra books use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue. Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must define ...
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 simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to ...