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- Mar 10, 2012

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I have been reading a book on Algebraic Geometry by Reid.

On page 15, there's a theorem on Quadratic forms. The book doesn't explicitly define what a Quadratic Form is. From Hoffman & Kunze's book on Linear Algebra I found that given an inner product space $V$ over a field $F$, the Quadratic Form determined by the inner product is a function from $V$ to $F$ which maps every vector $v\in V$ to the scalar $||v||^2$.

In the above context I can make sense of Theorem (B) in this:

https://docs.google.com/file/d/0B77QF0wgZJZ7VmhBcy1BaExTN28/edit

Does anybody see what Reid means by his Theorem B?