Witt's Theorem - Witt's Cancellation Theorem

Witt's Cancellation Theorem

Let (V, q), (V1, q1), (V2, q2) be three quadratic spaces over a field k. Assume that

Then the quadratic spaces (V1, q1) and (V2, q2) are isometric:

In other words, the direct summand (V, q) appearing in both sides of an isomorphism between quadratic spaces may be "cancelled".

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