# Linear Algebra Done Right

This best-selling textbook for a second course in linear algebra is aimed at undergrad 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.

## Linear Algebra Done Right

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The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.

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_OC_InitNavbar("child_node":["title":"My library","url":" =114584440181414684107\u0026source=gbs_lp_bookshelf_list","id":"my_library","collapsed":true,"title":"My History","url":"","id":"my_history","collapsed":true,"title":"Books on Google Play","url":" ","id":"ebookstore","collapsed":true],"highlighted_node_id":"");Linear Algebra Done RightSheldon AxlerSpringer Science & Business Media, Jul 18, 1997 - Mathematics - 251 pages 2 ReviewsReviews aren't verified, but Google checks for and removes fake content when it's identifiedThis text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents--without having defined determinants--a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. 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. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text. if (window['_OC_autoDir']) _OC_autoDir('search_form_input');Preview this book What people are saying - Write a reviewReviews aren't verified, but Google checks for and removes fake content when it's identifiedLibraryThing ReviewUser Review - cpg - LibraryThingKudos to Springer! Axler's linear algebra textbook is famously unusual for downplaying the use of determinants; in this edition, they don't really make an appearance until the very last section of the ... Read full review

Thnaks for making it clear that Axler is not intended for all undergrads who need linear algebra. I heartily approve of introducing the vector product basis free (right hand rule) but to calculate without 3 x 3 determinants?

My first course was explicitly matrix based, and avoided determinants were it could since they are no good for numerical calculations. As I remember it, other courses (mainly physics) had to work around our lack of basic linear algebra until we had caught up.

The course I took that tried using Axler as a text was not a sophomore-level linear algebra following on after the calculus sequence, but an upper-level course at the same level as a first course in abstract algebra. I think it might have even required abstract algebra as a co- or pre-requisite.

Although my field of research is analysis, some of my best friends are algebraicists who frequently use determinants in their research. So of course I know that determinants have many important uses in advanced mathematics such as some of the topics discussed on this blog. I do believe, however, that determinants have little utility for understanding elementary linear algebra (say at the level of my book).

That said, I was someone who understood zero, or close to zero, of the proofs I was shown in school. Now many years later, I get the point of doing things cleanly and basis-free, and something like this is perfect for improved, logical understanding. I think Axler is totally right to call it a second course in linear algebra.

Axler received the Lester R. Ford Award for expository writing in 1996 from the Mathematical Association of America for a paper titled "Down with Determinants!" in which he shows how one can teach or learn linear algebra without the use of determinants.[1] Axler later wrote a textbook, Linear Algebra Done Right (3rd ed. 2015), to the same effect.

Course description: Math 113 is a course on linear algebra, the study of vector spaces and linear maps. The emphasis will be quite theoretical: we will study abstract properties of vector spaces and linear maps as well as their geometric interpretation, mostly ignoring the computational aspects. If you are more interested in applications of linear algebra, you should consider taking Math 104 instead. Besides studying linear algebra, an important goal of the course is to learn how to write mathematics. In class we will give rigorous proofs, emphasizing proper mathematical language and notation. Through the homework assignments, you will learn to apply mathematical reasoning and write clear, compelling and correct proofs yourself. Your homework and exams will be judged accordingly. No background in linear algebra or proofs is assumed, and there are no formal prerequisites for the course; Math 113 is appropriate for students who have already seen some linear algebra in Math 51.

This is the final course in the linear algebra sequence. We cover all the material in MAT 211 (or AMS 210) as well as some material (for example the Cayley-Hamilton theorem and the Jordan canonical form) that will be new to most of you. The course will probably have quite a different emphasis from your previous courses on this subject: specific calculations will be of far less importance than understanding the statement of the main theorems and precisely why they are true. Because one of the aims of this course is to teach you how to write proofs, the homework and recitations are an integral part of the course. 041b061a72