Let K {\displaystyle {}K} be a field, and let V {\displaystyle {}V} denote a K {\displaystyle {}K} -vector space. A bilinear form
is called nondegenerate, if for every v ∈ V {\displaystyle {}v\in V} , v ≠ 0 {\displaystyle {}v\neq 0} , the induced mapping
and, for every w ∈ V {\displaystyle {}w\in V} , w ≠ 0 {\displaystyle {}w\neq 0} , the induced mapping
is not the zero mapping.