# Degenerate bilinear form

## From Wikipedia, the free encyclopedia

For other uses, see Degeneracy.

In mathematics, specifically linear algebra, a **degenerate bilinear form** *f* (*x*, *y* ) on a vector space *V* is a bilinear form such that the map from *V* to *V*^{∗} (the dual space of *V* ) given by *v* ↦ (*x* ↦ *f* (*x*, *v* )) is not an isomorphism. An equivalent definition when *V* is finite-dimensional is that it has a non-trivial kernel: there exist some non-zero *x* in *V* such that

- $f(x,y)=0\,$ for all $\,y\in V.$