Timeline for Linear Algebra Texts?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2013 at 1:04 | comment | added | Stefan | I thought the presentation of abstract material such as subspaces and inner product spaces was weak and relied excessively on matrix algebra. I know most students who aren't math majors hate this stuff and I don't know if there is any book that will make them like it.I admit I can't recommend another book. I used Strang's book once and, to put it positively, I'll say I much preferred Lay's (the only relative advantage is that Strang does cover the matrix exponential). | |
| Nov 2, 2013 at 1:00 | comment | added | Stefan | Presumably, since the proof requires projections, which are, I think, only defined for closed subspaces, Lay proves the Cauchy-Schwarz inequality only for subspaces of $\mathbb{R}^n$, though it is easy to prove for any inner product space. This is my opinion, but the definition of "vector space" includes unnecessary "closure" rules, which makes the intimidating list of rules even longer. The exponential of a matrix does not appear in the book at all. Consider that the book contains several semesters' worth of material, from what I have heard, this is a serious omission. | |
| Nov 2, 2013 at 0:54 | comment | added | Stefan | Lay has some serious flaws. He calls the dot product of two vectors in $\mathbb{R}^n$ "the inner product", as though this were the only inner product. I have gathered that this usage is common in the applied math world, but it is inappropriate in an introductory linear algebra book because you might want the students to learn the correct meaning of "inner product". The Cauchy-Schwarz Inequality is proven using projections, which is absurd, because all you need is some algebra and basic properties of inner product. The proof (using projections) is also more difficult than the usual proof. | |
| Sep 19, 2010 at 23:49 | comment | added | Dan Ramras | Now that I'm a month into the course, I think I can heartily say that I'm happy with the book. No, it isn't perfect, but quite often the complaints I have are addressed in the author's preface for instructors (in the instructor version) and several times I've become convinced that Lay has a good point, and there's a good reason for doing things the way he does. It's very tempting to lay on tons of concepts early on in a linear algebra course. Lay's book is good about introducing concepts slowly, and then reinforcing them later with new viewpoints. | |
| Sep 19, 2010 at 23:46 | vote | accept | Dan Ramras | ||
| May 24, 2010 at 22:22 | comment | added | Victor Protsak | Mark it as the right answer, then:) This book isn't perfect, but I liked it a lot and I hope that so will you and your students. | |
| May 24, 2010 at 19:18 | comment | added | Dan Ramras | In the end, this is the book I decided to go with. | |
| May 23, 2010 at 1:46 | history | answered | Victor Protsak | CC BY-SA 2.5 |