Given a finite-dimensional non-zero purely odd super-vector space with non-degenerate super-symmetric pairing $(-,-)$, that is $(x,y)=-(y,x)\quad\forall x,y$.
How does this imply that this super-vector space is even dimensional?
Given a finite-dimensional non-zero purely odd super-vector space with non-degenerate super-symmetric pairing $(-,-)$, that is $(x,y)=-(y,x)\quad\forall x,y$.
How does this imply that this super-vector space is even dimensional?
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