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Please suggest a Linear Algebra book with an introduction and rigorous theory (description) on Eigenvectors , eigen-values , Cayley-Hamilton theorem , Diagonalisation of matrices ; Quadratic forms ( Sylvester's Law , rank , signature , reduction to canonical forms ) .

Thanks in advance

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    $\begingroup$ Related. $\endgroup$ – Hakim Aug 3 '14 at 14:19
  • $\begingroup$ Are you looking for a book for self study? Or are you looking to push ahead in a university course? There are plenty of fantastic Linear Algebra books out there - if you're looking to get ahead in university, I'd suggest looking at your university's subject page for linear algebra, where I'm sure there'll be some suggestions that fit your university's approach to the subject. $\endgroup$ – Mathmo123 Aug 3 '14 at 14:19
  • $\begingroup$ @Mathmo123: I am looking for a book to self-study $\endgroup$ – Souvik Dey Aug 3 '14 at 14:28
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I suggest Linear Algebra by Serge Lang. I studied those arguments using that book and it's excellent.

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I suggest Linear Algebra by Hoffman and Kunze which covers those topics and have some excellent exercises

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A very good first course (for mathematically solid students) is Sergei Treil's "Linear Algebra Done Wrong." There is a reason for the odd name, described in the link. Here is the text. Best of all: IT'S FREE!

If you have seen some linear algebra, and you want an introduction to the coordinate-free approach, check out this (ALSO FREE!) cool book by Sergei Winitzki called "Linear Algebra via Exterior Products." You'll likely find it challenging, but it's worth the trouble.

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    $\begingroup$ We used Treil's book in my LA course last spring. Good book but his typos are quite frustrating at times. Nonetheless felt that it was quite enlightening and was more than worth printing the first 6 chapters. $\endgroup$ – Austin Stromme Aug 3 '14 at 18:01
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    $\begingroup$ @AustinStromme: Be sure to send Prof. Treil an email of any typos you find that aren't already on the errata list! It's the least we can do to show our appreciation for sharing such a great book with us. $\endgroup$ – user59083 Aug 3 '14 at 18:25
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I think these are some well written and helpful books on the subjects you mentioned:

All of them provide solutions to every single problem they present, so they're particularly appropriate for self-study.

The first two, by Blyth and Robertson, are a little bit more compact while the book by Meyer feels more like a bible; that being said, Meyer's book has lots of solved examples and applications to motivate the theory and, in my opinion, it is still quite strong on the theoretical side.

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