Bilinear Algebra: An Introduction to the Algebraic Theory of Quadratic Forms, Vol. 7 Book

	Preface
Pt. I	Bilinear spaces	1
1	Introduction	3
2	Bilinear spaces	15
3	Bases and matrices of bilinear spaces	25
4	Isometries of bilinear spaces	35
5	Nonsingular bilinear spaces	47
6	Diagonalization of bilinear spaces	63
7	Witt's cancellation theorem	75
8	Witt's chain isometry theorem	87
9	Symmetric spaces over some fields	101
10	Isometry groups	113
Pt. II	Witt rings	129
11	Metabolic and hyperbolic spaces	131
12	Witt decomposition of symmetric spaces	147
13	Witt group	163
14	Tensor products	175
15	Witt ring	191
16	Quadratic forms	207
17	Pfister forms	229
18	Formally real fields and ordered fields	249
19	Prime ideals of the Witt ring	275
20	Witt equivalence of fields	303
Pt. III	Invariants	321
21	Algebras	323
22	Quaternion algebras	341
23	Tensor product of algebras	365
24	Brauer group	387
25	Hasse and Witt invariants	403
A	Symbolic Hasse and Witt invariants	425
B	Selected problems	439
	Bibliography	471
	Notation	479
	Index	482