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searching for Degenerate bilinear form 12 found (15 total)

alternate case: degenerate bilinear form

Eisenbud–Levine–Khimshiashvili signature formula (1,722 words) [view diff] exact match in snippet view article find links to article

vector field X at 0 is given by the signature of a certain non-degenerate bilinear form (to be defined below) on the local algebra BX. The dimension of

Musical isomorphism (4,149 words) [view diff] exact match in snippet view article find links to article

finite-dimensional vector space V {\displaystyle V} endowed with a non-degenerate bilinear form ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is canonically

CCR and CAR algebras (1,380 words) [view diff] exact match in snippet view article find links to article

anticommutation relations in terms of a symplectic and a symmetric non-degenerate bilinear form. In addition, the binary elements in this graded Weyl algebra give

Triality (771 words) [view diff] exact match in snippet view article find links to article

3D4. A duality between two vector spaces over a field F is a non-degenerate bilinear form V 1 × V 2 → F , {\displaystyle V_{1}\times V_{2}\to F,} i.e., for

Goddard–Thorn theorem (1,270 words) [view diff] exact match in snippet view article find links to article

\mathrm {Vir} } , so V {\displaystyle V} is equipped with a non-degenerate bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} and there is an algebra

Linear form (5,966 words) [view diff] exact match in snippet view article find links to article

realized as linear functionals on spaces of test functions. Every non-degenerate bilinear form on a finite-dimensional vector space V induces an isomorphism V

Duality (mathematics) (6,694 words) [view diff] exact match in snippet view article

finite-dimensional. In this case, such an isomorphism is equivalent to a non-degenerate bilinear form φ : V × V → K {\displaystyle \varphi :V\times V\to K} In this case

Integral element (5,304 words) [view diff] exact match in snippet view article find links to article

easy and standard (uses the fact that the trace defines a non-degenerate bilinear form). Let A be a finitely generated algebra over a field k that is

Metric tensor (8,863 words) [view diff] exact match in snippet view article find links to article

Conversely, any linear isomorphism S : TpM → T∗ pM defines a non-degenerate bilinear form on TpM by means of g S ( X p , Y p ) = [ S X p , Y p ] . {\displaystyle

Clifford algebra (9,287 words) [view diff] exact match in snippet view article find links to article

from the Euclidean metric on R3. For v, w in R4 introduce the degenerate bilinear form d ( v , w ) = v 1 w 1 + v 2 w 2 + v 3 w 3 . {\displaystyle d(v

Cross product (11,568 words) [view diff] exact match in snippet view article find links to article

inner product (such as the dot product; more generally, a non-degenerate bilinear form), we have an isomorphism V → V ∗ , {\displaystyle V\to V^{*},}

Minkowski space (10,458 words) [view diff] exact match in snippet view article find links to article

space of standard bases from different sides. Technically, a non-degenerate bilinear form provides a map between a vector space and its dual; in this context