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