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I am considering among "Linear Algebra Done Right", "Linear Algebra" of Kenneth Hoffmann And Ray Kunze, and "Linear Algebra" of Lang, once I finish the book of Friedberg? The purpose is to prepare for studying the book Convex Optimization of Boyd.

Thanks,

Arturo Magidin
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Jesse
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    Axler isn’t going to give you anything you don’t get out of Friedberg/Insel/Spence; at most, it will give you a different view (and a determinant-free view, as that is the main point of the book). You aren’t going to get a “more advanced view” out of it. – Arturo Magidin Dec 15 '19 at 00:46
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    (And Serge Lang is not generally known as an author you want to learn from... other than his books on material that is not available elsehwere, like his Diophantine Analysis book, he’s not particularly didactical, even if he is sometimes encyclopedic) – Arturo Magidin Dec 15 '19 at 00:47
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    Boyd has an appendix (A.5) that seems to at least outline what linear algebra it needs. My mildly educated guess would be that Hefferon and Treil plus some googling on the Schur complement (which isn't often treated in textbooks anyway) should suffice. – darij grinberg Dec 15 '19 at 01:05
  • Does this answer your question? High-level linear algebra book –  Apr 26 '23 at 03:24

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If the goal is to prepare to read Convex Optimization by Boyd and Vandenberghe, then you don't need anything more advanced than Friedberg. Go ahead and dive in to Convex Optimization now. You certainly do not need to read Hoffman and Kunze!

It might be helpful, though, to read a linear algebra book that is written from the perspective of an applied mathematician. I recommend specifically Gilbert Strang's book An Introduction to Linear Algebra, or alternatively Strang's book Linear Algebra and Its Applications. Personally, I studied Friedberg first, but when I read Strang's books I found them to be filled with very helpful insights. Things which had seemed a bit abstract previously now seemed simple and obvious.

Boyd and Vandenberghe themselves have written a linear algebra book called Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares, which is free online. This book is simple and clear and teaches most of the linear algebra you need to read Convex Optimization.

I also recommend Numerical Linear Algebra by Trefethen, which covers useful topics in numerical linear algebra which are not touched on in Friedberg.

While the books I mentioned above are not more advanced than Friedberg, the applied perspective is valuable. If you do wish to read a book that is more advanced than Friedberg, I agree that Linear Algebra Done Right is worth reading, and I'm also a big fan of Linear Algebra and Its Applications by the great mathematician Peter Lax.

littleO
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  • Be careful. Boyd claims that vector spaces are occasionally used in his Convex Optimization, but they don't ever appear in Boyd/Vandenberghe. And I wouldn't recommend Axler to anyone who doesn't already know the correct definition of a polynomial well enough to avoid getting misguided. – darij grinberg Dec 15 '19 at 01:06
  • @darijgrinberg "but they [vector spaces] don't ever appear in Boyd/Vandenberghe." That comment seems to be consistent with the recommendations I gave, I think. The books I recommended as preparation for Boyd & Vandenberghe don't emphasize abstract vector spaces. – littleO Dec 15 '19 at 01:12
  • Oh, I just realized both books are by both authors, which renders my way of referencing them useless :) I meant that vector spaces don't appear in their linear algebra book but are used in their convex optimization book, so the former is not a sufficient preparation for the latter. – darij grinberg Dec 15 '19 at 01:14
  • @darijgrinberg Oh I see. But, Convex Optimization by Boyd and Vandenberghe mainly works in $\mathbb R^n$. I think they sometimes work with $S_m$, the space of real symmetric $m \times m$ matrices, but even then I believe $S_m$ is identified with $\mathbb R^n$ in a certain way, so that readers who are only comfortable working in $\mathbb R^n$ will still be ok. Boyd and Vandenberghe tend to keep things rather concrete. – littleO Dec 15 '19 at 01:17
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I don’t know how it matches up with Boyd, but one possibility if you want a more abstract view point is Roman’s “Advanced Linear Algebra”, in the GTM series.

Arturo Magidin
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