Can anyone recommend a good reference for brushing up on quadratic forms?
They keep coming up (quite naturally of course) in the context of differential geometry and I find I am rustier than I remembered. I've looked through a large number of linear algebra books and found mostly short sections that cover the basics: reduction to canonical form and Sylvester's criterion, but nothing that goes much beyond. I've also found others that get quite deep into the issue from a more abstract algebraic point of view, but they seemed like they would require a significant detour from my current studies. Does anyone know any books that provide something in between?
(Something available as a pdf that I can download/buy online would be perfect, but any other reference would help greatly as well).
Thanks in advance
Best Answer
Here are three PDFs that I became aware of during my own searches on this question some time ago:
http://www.math.jussieu.fr/~karpenko/publ/Kniga.pdf
http://www.math.miami.edu/~armstrong/685fa12/pete_clark.pdf
http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/bilinearform.pdf
I think a "middle" text that is both affordable and easy to obtain is Jacobson's Basic Algebra I Chapter 6 on metric vector spaces.
T.Y. Lam's Introduction to quadratic forms also sounds like a good bet. I say that because I haven't read this book yet, but judging from the author's other books, I bet this one must be good too. Good luck!