Quotient quadratic space
Let
Properties
- The quotient vector space
π / π π
Proof of 1.
For the quadratic form to be well defined, we require
for all π ( π£ + π’ ) = π ( π£ ) and π£ β π . Equivalently π’ β π 0 = π ( π£ + π’ ) β π ( π£ ) = π π ( π£ , π’ ) + π ( π’ ) for all
and π£ β π . This includes, however, that π’ β π , so any such 0 = π ( 0 + π’ ) = π ( π’ ) must be both degenerate and ^isotropic. π’