# non-degenerate bilinear form

A bilinear form $B$ over a vector space $V$ is said to be non-degenerate when

• if $B({{\bf x}},{{\bf y}})=0$ for all ${{\bf x}}\in V$, then ${{\bf y}}={{\bf 0}}$, and

• if $B({{\bf x}},{{\bf y}})=0$ for all ${{\bf y}}\in V$, then ${{\bf x}}={{\bf 0}}$.

 Title non-degenerate bilinear form Canonical name NondegenerateBilinearForm Date of creation 2013-03-22 12:25:56 Last modified on 2013-03-22 12:25:56 Owner djao (24) Last modified by djao (24) Numerical id 5 Author djao (24) Entry type Definition Classification msc 47A07 Classification msc 15A63 Classification msc 11E39 Synonym non-degenerate form Synonym nondegenerate bilinear form Synonym nondegenerate form Synonym non-degenerate Synonym nondegenerate