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There's a introductory book that I would add to the "generalist" list, that is 'Linear Algebra Done Wrong' by Sergei Treil. It can be found freely here: https:/
by doppioandante 10y ago
There's a introductory book that I would add to the "generalist" list, that is 'Linear Algebra Done Wrong' by Sergei Treil.
It can be found freely here: https://www.math.brown.edu/~treil/papers/LADW/LADW.html https://www.math.brown.edu/~treil/papers/LADW/LADW.html
I've used it to prepare my linear algebra exam in an italian university (which usually emphasize theory over practice, even in engineering courses), and I've loved it.
There are few exercises but they're to the point. Complex inner product, self-adjoint operators etc. are treated. I find the notation used in there particularly easy to understand, and proofs are elegant but very easy to follow.
- begriffs 10y agoI was on the fence about that one and ultimately took it off the list. It seems to be fairly numerical, sort of in defiance to Axler's "Done Right" book. But then as a numerical book how does it compare with the others in that category, or with the old Russian books? I ask quite honestly because I haven't gone through Treil's book. Does it hold its own?
- doppioandante 10y agoActually, I think it's very similar to Axler's in spirit. Not numerical at all (there is a description of the min squares problem, but that's it as far as I remember). Matrices are used more explicitely than in Axler, but only when necessary, because the author claims he's an operator theorist so the focus is on linear operators. Determinants are introduced as multi-linear functionals and are not avoided as in Axler. Supporting the fact that the book is quite theoretical, this is what you can find in the last chapters: Chapter 6. Structure of operators in inner product spaces. Chapter 7. Bilinear and quadratic forms Chapter 8. Dual spaces and tensors Chapter 9. Advanced spectral theory Unfortunately I'm not familiar with the Russian books.
- znpy 10y agoI have skimmed some books about Linear Algebra, both in Italian and in English, and my favourite so far is "Geometria e Algebra Lineare" by Enrico Schlesinger. The book is very well written but sadly it won't be enough to pass a typical italian Linear Algebra exam. This is because, in my opinion, examples are too vague or too "abstract": when you're first learning such subject, it would be better to have layman terms, that is simple examples with simple numbers. More complex examples might be okay too, but simple examples should come first. Reference: http://www.zanichelli.it/ricerca/prodotti/algebra-lineare-e-geometria http://www.zanichelli.it/ricerca/prodotti/algebra-lineare-e-...
- ndr 10y agoMarco Abate's "Geometria" was also quite entertaining.
- doppioandante 10y agoMy favourite linear algebra book in italian is "Geometria e Algebra Lineare" by Abbena, Finno and Giannella. Really great book, with a wealth of exercises and extensive material. I can also suggest the youtube lectures[0] by Francesco Bottacin, who actually was the one that eventually did my oral examination. He's also written two books based on the course, the one with exercises[1] is very solid and I think you can pass the written exam by just doing it whole. They told me he is a wonderful lecturer. Pity that all this material is in italian. [0] https://www.youtube.com/channel/UCpJGeVBfmf-6S3neeImAw1w/feed https://www.youtube.com/channel/UCpJGeVBfmf-6S3neeImAw1w/fee... [1] https://www.amazon.it/Esercizi-algebra-geometria-Francesco-Bottacin/dp/8874889305?ie=UTF8&SubscriptionId=AKIAJALSGXBDME3OOGUQ&camp=2025&creative=165953&creativeASIN=8874889305&linkCode=xm2&tag=esculapio-21 https://www.amazon.it/Esercizi-algebra-geometria-Francesco-B...
- x0x0 10y agoYou'd probably like Strang. He's an mit professor who shared his linear algebra course lectures. They're excellent. http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/ http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-... A one-edition back version of his book _Introduction to Linear Algebra_ is available for under $30. https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-Strang/dp/0961408898/ref=sr_1_1?s=books&ie=UTF8&qid=1469389149&sr=1-1&keywords=introduction+to+linear+algebra+3rd+strang https://www.amazon.com/Introduction-Linear-Algebra-Gilbert-S...
- doppioandante 10y agoUnfortunately that book was too lightweight on theory to be of use to me, but it's certainly a very good book. I've recently started Strang's more advanced book on computational linear algebra/numerical analysis and it's pretty good though.
- samblr 10y agoLinear Algebra Done Wrong is quoted at many places with another book - Linear Algebra Done Right. Did you study other book - any thoughts?
- deleted 10y ago[deleted]