Could anyone possibly help me find a classification of quadratic forms in n-dimensional Euclidean space? I would very much appreciate a link or paper or book.
Here some books about Quadratic Forms:
O'Meara, O.T. (2000), Introduction to Quadratic Forms, Berlin, New York: Springer-Verlag, ISBN 978-3-540-66564-9
Shafarevich, I. R.; A. O. Remizov (2012). Linear Algebra and Geometry. Springer. ISBN 978-3-642-30993-9.
Lam, Tsit-Yuen (2005). Introduction to Quadratic Forms over Fields. Graduate Studies in Mathematics 67. American Mathematical Society. ISBN 0-8218-1095-2. MR 2104929. Zbl 1068.11023.
Cassels, J.W.S. (1978). Rational Quadratic Forms. London Mathematical Society Monographs 13. Academic Press. ISBN 0-12-163260-1. Zbl 0395.10029.
Kitaoka, Yoshiyuki (1993). Arithmetic of quadratic forms. Cambridge Tracts in Mathematics 106. Cambridge University Press. ISBN 0-521-40475-4. Zbl 0785.11021.
Here is a set of articles that may be of interest to followers of this thread:
E. Bayer-Fluckiger, D. Lewis, A. Ranicki, Eds., Quadratic Forms and Their Applications, Proc. Conf. on Quadratic Forms, University College Dublin, 1999:
http://www.maths.ed.ac.uk/~aar/books/dublin.pdf
More recently, we have
J.S. Milne. Algebraic Geometry, 2009, 245 pages:
http://www.jmilne.org/math/CourseNotes/AG520.pdf
Classifying quadratic forms starts on page 176.
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