Linear Algebra Completed Proper Guide Assessment



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26 thoughts on “Linear Algebra Completed Proper Guide Assessment”

  1. So you're reviewing this book but haven't actually read it? Is this just to get clicks on your affiliate link?

    The only difference between this book and other textbooks is it's got pictures and coloured boxes. The fact it "highlights the important things", "puts examples", and "proof worked out right for you" is what every math textbook does.

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  2. Thank you Brian! Currently taking proof based-linear algebra in undergrad (and using Friedberg and Insel’s a bit more obscure book) this one is a very nice help sometimes 🙂

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  3. Hey i was searching for a book to buy for autodidact purpose. Nothing too much complicated but complete. Is this completed with exercises?
    There are others like introduction to Linear algebra by Gilbert Strang and linear algebra by Serge Lang which they say are really good books

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  4. Good video. Yet, I kind of disagree about this book. This is a bit of a misnomer calling a book that way and doing exactly the opposite. It should be called Linear Algebra Done Wrong: Making Dumbed-Down Incomplete Coverage Look Advanced (just skip on proofs and theory — people don't get it anyway). We need another dumbed-down book to cover the rest. Just my opinion. Sorry for the harsh criticism of the book. Now I think that the best first book on Linear Algebra is Elementary Linear Algebra by Kolman. The second best (simpler and shorter) is the book by Gilbert Strang. Kolman's text is not very difficult, not too rigorous, not too dumbed-down or non-rigorous. It has derivations, proofs, explanations, applications and all the basics — around 500-700 pages. Great book. Will work nice with Abstract Algebra by Fraleigh but doesn't require any presupposed knowledge from the reader beyond university calculus. You don't need Abstract Algebra, of course because it's overkill unless you are going to be a mathematician. Well, Kolman is self-sufficient. Not abstract at all but do have all the basics on vector spaces. However for more abstract topics and more depth, I would add Serge Lang's books on Linear Algebra if Kolman is not enough (Kolman is not enough for math majors cause you need a lot of abstract algebra, you need tensors, you need tons of stuff if you want to be a truly pro mathematician). For everybody else, Kolman is perfect, and although it might be a bit challenging it's very healthy for studying hard and for gaining a true understanding without going too far into advanced math. Studying Kolman is very rewarding but it's not a dumbed-down waltz-through. You need to work with the book very seriously. It is similar to Sheldon Ross's book First Course in Probability (an excellent book for true understanding of Probability Theory) and DiPrima's book on ODE. These are all topnotch classical books if we have time to really master those areas (usually people just study very, very superficially). Non-mathematicians don't really need abstract algebra but those who want or need it (also rewarding but a different experience!) can study Abstract Algebra by Fraleigh (one of my favorite books). It's not difficult as far as books on abstract algebra go. it's only around 600 pages long — so it's doable if you want to be like 'the sky is my limit' but it's just the tip of the iceberg, just a peek through a spy-hole into modern math, and it can be your first revelation, while Linear Algebra Done Right by Axler is obfuscation, cutting down on crucial material, putting on airs (of being advanced while being stupid) = a path for rote-learning and snobbery. Once again, sorry for criticism of the book but I doubt people will ever learn anything from it besides memorizing things. There are almost no explanations, no derivations and huge gaps — too huge for making even a little bit coherent picture out of linear algebra. The author recommends: You may cover chapter 4 and 9 in fifteen minutes each…. I mean why even bother…. Goes in one ear out the other. It's not even rote-learning. It's a joke. Absence of answers and very few worked problems in sections should also be criticized. But I don't criticize his approach eschewing determinants, nor do I criticize 'verify yourself' or 'fill in the skipped steps' in the proofs given by the author — it's not a bad practice, and if done right it is a good thought-provoking tool reducing rote-learning, but I'm afraid it was botched up too in this book. Well, it could have been a good book but it is not. In my opinion it's a disaster for a future mathematician. For non-mathematicians and rote-learners it should be fine. Such short books are no go when they try to cover too much. The irony is that it supposedly targets future mathematicians but they will be fine anyway 'cause they have dozens if not hundreds of math books anyway. I'd give this book no more than 2 stars out of 5.

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  5. But the book only does things over C and R. I feel like that is a pretty bad thing, as vector spaces over other fields are important for both mathematicians and people who apply math alike

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  6. As far as I’m concerned, and with all due respect to Mr. Axler, his little yellow book doesn’t live up to what its title claims. He doesn’t do any linear algebra. He wastes the reader’s time by writing trite phrases like: The verification…is easy. It’s easy to see… The proof is left to the reader. I understand he was a good boy at Princeton University, and I hope he enjoys his boasting about the Lester R. for Award he, I’m sure, deservedly obtained. But if you’re struggling with linear algebra, I’d advise you to buy any other book from anyone else, except from him, since Mr. Axler doesn’t have an idea of what pedagogy is. Indian mathematicians, from my point of view, are the best tutors on earth. Although their books are expensive. If you don’t have the money or if you don’t want to buy an expensive book, you can buy “Introduction to Linear algebra” by Casteleiro Villalba, to start with. Besides, you can download, for free, “Linear Algebra Step by Step” by Singh.

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