A nondegenerate bilinear form 
on a finite-dimensional vector space 
over a field 
is a bilinear form for which
 |
implies 
,
and likewise with the two arguments interchanged. Equivalently,
the associated linear map 
is an isomorphism,
where 
is the dual vector space. In a vector
basis, this is equivalent to the matrix of 
being a nonsingular matrix.
