| 41. | When studying vector spaces or related stuff in application, bilinear forms defined on them are often useful and indispensable.
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| 42. | The signature of this non-degenerate bilinear form being equal to the index of " X ".
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| 43. | In functional analysis a "'Dirichlet forms "'form a class of bilinear forms function spaces.
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| 44. | If is a real vector space, then we replace by its complexification and let denote the induced bilinear form on.
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| 45. | Weyl algebras represent the same structure for symplectic bilinear forms that Clifford algebras represent for non-degenerate symmetric bilinear forms.
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| 46. | Weyl algebras represent the same structure for symplectic bilinear forms that Clifford algebras represent for non-degenerate symmetric bilinear forms.
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| 47. | Since for an antiautomorphism we have for all in, if, then must be commutative and is a bilinear form.
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| 48. | Formally, the analogy is stated as a symmetric bilinear form ( multiplication ) and a quadratic form ( squaring ).
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| 49. | To do something like this in general, we can use any bilinear form, but that involves more structure than just
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| 50. | A "'quadratic Lie algebra "'is a Lie algebra together with a compatible symmetric bilinear form.
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