31. The matrix corresponding to this bilinear form ( see below ) on a standard basis is the identity matrix. 32. By the properties of definite integrals, this defines a symmetric bilinear form on " V ". 33. Define a non-degenerate anti-symmetric bilinear form on the-1 graded piece by the rule: 34. A bilinear form on " D " arises by pairing the image distribution with a test function. 35. Littlewood's 4 / 3 inequality on bilinear forms was a forerunner of the later Grothendieck tensor norm theory. 36. A bilinear form " B " is reflexive if and only if it is either symmetric or alternating. 37. An analogous statement holds also for skew-symmetric, Hermitian and skew-Hermitian bilinear forms over arbitrary fields. 38. Also, given a coercive self-adjoint operator A, the bilinear form a defined as above is coercive. 39. This is easy and standard ( uses the fact that the trace defines a non-degenerate bilinear form .) 40. "' Explanation of occurrence of the fields "': There are no nontrivial bilinear forms over.
