Editing Degenerate bilinear form (section)

==Using the determinant==
If ''V'' is finite-dimensional then, relative to some [[basis (linear algebra)|basis]] for ''V'', a bilinear form is degenerate if and only if the [[determinant]] of the associated [[matrix (mathematics)|matrix]] is zero – if and only if the matrix is ''[[singular matrix|singular]]'', and accordingly degenerate forms are also called '''singular forms'''. Likewise, a nondegenerate form is one for which the associated matrix is [[non-singular matrix|non-singular]], and accordingly nondegenerate forms are also referred to as '''non-singular forms'''. These statements are independent of the chosen basis.