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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 determinants via alternating multilinear forms. This new edition also increases the use of the minimal polynomial to provide cleaner proofs of multiple results. Also, over 250 new exercises have been added. 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 simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. Beautiful formatting creates pages with an unusually student-friendly appearance in both print and electronic versions. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. 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 introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator. From the reviews of previous editions: Altogether, the text is a didactic masterpiece . โ zbMATH The determinant-free proofs are elegant and intuitive . โ American Mathematical Monthly The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library โ CHOICE Review: Fills in the gap! - Got this book for my son who is a math major in college. It help bridge the gap between the teaching and book learning. Review: Linear Algebra! - Classic Linear Algebra college course book. Highly recommend to get hold of one.
| Best Sellers Rank | #17,661 in Books ( See Top 100 in Books ) #2 in Linear Algebra (Books) #4 in Algebra & Trigonometry |
| Customer Reviews | 4.7 out of 5 stars 276 Reviews |
R**N
Fills in the gap!
Got this book for my son who is a math major in college. It help bridge the gap between the teaching and book learning.
P**3
Linear Algebra!
Classic Linear Algebra college course book. Highly recommend to get hold of one.
M**C
A good book to relearn Linear Algebra
Heard of this book many times. This is a great book for me to relearn Linear Algebra. The price is reasonable for a new book.
A**V
An in-depth treatment
For those of you who wish to really know whats behind those elementary, middle school silliness of matrices truly and understand vectors, use two things: 1. This book 2. ChatGPT This book will give you a really solid foundation of: 1. Vector and vector spaces 2. Linear Maps and matrices 3. Eigenvalues and EigenVectors And linear algebra in general. I wish Iโd read this book in my elementary - Iโd have more interest in math if I did. Remember to really ask questions with your choice of AI - mine is ChatGPT - combining this book with a dialog and doing problems can really clarify a lot of things. Good luck!
E**A
Muy bien
Llegรณ en muy buenas condiciones, tal como esperaba. Pero sรญ veo que Amazon debe mejorar las condiciones del empaque, ya que la caja en la que vienen los libros es mรกs grande que รฉstos, y podrรญan maltratarse, ya que no tienen ninguna otra protecciรณn. Afortunadamente mis libros han llegado sin problemas. Pero respecto al libro, excelente.
C**A
High quality print
High quality print. The language/explanations tend to be a little over my head, though.
A**N
Wonderful book
I am a graduate student who studies an area steeped in linear algebra. I have found this book invaluable, particularly the author's hard work on making proofs elegant and readable. I had bought a copy of the third edition previously, but I bought the fourth edition because I greatly appreciate the Axlerization of the tensor product (which I live and breathe) in the last chapter.
O**K
Single author tour de force!
Aesthetically stunning.
G**R
Excellent ouvrage
Excellent ouvrage Indispensable pour รฉtudiants en maths
V**R
Good book
Good and interesting book
J**N
linear algebra revision
Good revision of the topic
D**A
Linear Algebra: As clear and elegant as it should be
As someone who has taugh univesity-level physics for the last twelve years and have spent another ten years with undergraduate and graduate studies, I can confidently say that no other book, either in physics or mathematics, has excited me as much as this one in recent years. I picked up this book to refresh my knowledge on Linear Algebra while preparing a course on Quantum Mechanics, and I felt that it is pure joy! It became one of my favorite books. The reason is that this book is formal, cristal clear, logical and abstract. Many widely used Linear Algebra textbooks today seem to fail in at least one of these aspects. There is always an oversimplification that teaches pieces or processes and not the whole. While many of these books reduce Linear Algebra to a collection of procedures with lists, matrices and specific techniques such as orthogonalizations, diagonalizations, reductions, etc, Mr. Axler was definitely successfull in showing what Linear Algebra is about - linear spaces and operators - and how to properly and elegantly teach it. Last but not least, hats off to the author and Springer for making this book open access. And for those considering buying the physical copy, definitely do it if you can afford it. A PDF file will never give you the feeling of a friend the way a physical book does.
F**.
Personal Review of Linear Algebra Done Right
Coming from this prestigious editor, this book contains the very essence of linear algebra but explained in a very mathematical way. Itโs great for undergraduates that aim for a more complex mathematical and yet, not so simple understanding. I recommend it highly to those who are looking for the most challenging mathematical approach. Great for undergraduate mathematicians and physics majors.
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