Editing Degenerate bilinear form (section)

==Infinite dimensions==
{{Disputed section|Which dual space?|date=May 2025}}
Note that in an infinite-dimensional space, we can have a bilinear form ƒ for which <math>v \mapsto (x \mapsto f(x,v))</math> is [[injective]] but not [[surjective]].  For example, on the space of [[continuous function]]s on a closed bounded [[interval (mathematics)|interval]], the form 
:<math> f(\phi,\psi) = \int\psi(x)\phi(x) \,dx</math> 
is not surjective: for instance, the [[Dirac delta functional]] is in the dual space but not of the required form.  On the other hand, this bilinear form satisfies 
:<math>f(\phi,\psi)=0</math> for all <math>\phi</math> implies that <math>\psi=0.\,</math>
In such a case where ƒ satisfies injectivity (but not necessarily surjectivity), ƒ is said to be ''weakly nondegenerate''.{{cn|date=May 2025}}