5 ms·
The book is open access (https://linear.axler.net/ https://linear.axler.net/), I am going to quote directly the author in the preface: << all linear algebra bo
by mseri 4y ago
The book is open access (https://linear.axler.net/ https://linear.axler.net/), I am going to quote directly the author in the preface:
<< 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 determinants, prove that a linear map is not invertible if and only if its determinant equals 0, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues exist.
In contrast, the simple determinant-free proofs presented here (for example, see 5.21) offer more insight. Once determinants have been banished to the end of the book, a new route opens to the main goal of linear algebra— understanding the structure of linear operators.>>
If you like mathematics, it is actually a pretty nice book.
- na85 4y agoI don't believe it's open access, or at least I see no download link on that page.
- BeetleB 4y agoI don't see the link either, but I also do recall him releasing it for free. You can find it on the Internet Archive: https://archive.org/details/SheldonAxlerAuth.LinearAlgebraDoneRight https://archive.org/details/SheldonAxlerAuth.LinearAlgebraDo...
- nextos 4y agoThe philosophy of LADR is described in his paper Down with determinants: https://www.axler.net/DwD.html https://www.axler.net/DwD.html. In short, he thinks they obscure proofs. I love the book, but AFAIK only the compactified version (excluding all proofs, examples, and exercises, along with most comments) is open access: https://linear.axler.net/LinearAbridged.pdf https://linear.axler.net/LinearAbridged.pdf. IMHO, since the OP wants to apply linear algebra to real world problems, a better approach is to go with a matrix analysis book. Strang is very popular, but my favorite is http://matrixanalysis.com/Contents.html http://matrixanalysis.com/Contents.html. Axler is a few notches higher in terms of abstraction. Hence, you won't learn lots of important practical results about matrices. In case of going with Axler, I'd use the previous edition. It's a shame they have ruined the typesetting by adding so many distracting color boxes and different fonts. Personally, I'd go with Hubbard & Hubbard: https://matrixeditions.com/5thUnifiedApproach.html https://matrixeditions.com/5thUnifiedApproach.html. It's a work of art that takes you from pre-calculus till multivariate calculus and analysis, along with all necessary linear algebra. Great mix of rigor, intuitions and practical details. At this level, as Hubbard points out, it's very useful to combine linear algebra with calculus & real analysis.
- gww 4y agoWould Hubbard and Hubbard be too difficult if I found Spivaks calculus too difficult? I have been struggling to find a linear algebra book that isn't too abstract or too verbose. I did take LA and calculus a decade ago and I am trying to build up a background strong enough for probability and statistics.
- nextos 4y agoIt depends. Skim through H&H to see. I find it more intuitive and modern, but it also covers way more territory. At some point, the material will be hard because it's very advanced mathematics. However, by then perhaps you have already adjusted. There's also a solution manual. Furthermore, many difficult proofs are in the appendix. So it's more of a calculus book if you want to ignore the analysis part.
- gww 4y agoThanks for the reply I will definitely go check it out. I don't mind putting in the time and effort and a solution manual will definitely help.
- nextos 4y agoNo worries. Are you aiming at statistics? If so, what branch? There might be other quicker ways to bootstrap. Then, you can come back to H&H.