= Alternating bilinear form
{title2=$B(v,v)=0$}
A <bilinear form> is alternating if $B(v,v)=0$ for every <vector> $v$. Expanding $B(v+w,v+w)$ implies $B(v,w)=-B(w,v)$. The converse requires <characteristic> different from two. In that characteristic a skew-symmetric <matrix> of <odd integer> size has zero <determinant>, since $\det A=\det(-A^T)=(-1)^n\det A$. Thus an alternating form on a finite odd-dimensional <vector space> is degenerate. A <nondegenerate> alternating form defines a <symplectic vector space>.
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