- signature of quadratic form
- сигнатура квадратичной формы
English-Russian scientific dictionary. 2008.
signature of quadratic form
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Quadratic form — In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, is a quadratic form in the variables x and y. Quadratic forms occupy a central place in various branches of mathematics, including… … Wikipedia
Isotropic quadratic form — In mathematics, a quadratic form over a field F is said to be isotropic if there is a non zero vector on which it evaluates to zero. Otherwise the quadratic form is anisotropic. More precisely, if q is a quadratic form on a vector space V over F … Wikipedia
Signature (mathematics) — In mathematics, signature can refer to*The signature of a permutation is ±1 according to whether it is an even/odd permutation. The signature function defines a group homomorphism from the symmetric group to the group {±1}. *The signature of a… … Wikipedia
Signature (topology) — In mathematics, the signature of an oriented manifold M is defined when M has dimension d divisible by four. In that case, when M is connected and orientable, cup product gives rise to a quadratic form Q on the middle real cohomology group: H 2 n … Wikipedia
Signature of a knot — The signature of a knot is a topological invariant in knot theory. It may be computed from the Seifert surface.Given a knot K in the 3 sphere, it has a Seifert surface S whose boundary is K . The Seifert form of S is the pairing phi : H 1(S) imes … Wikipedia
Signature operator — Let X be a 4k dimensional compact Riemannian manifold. The signature operator is a elliptic differential operator defined on a subspace of the space of differential forms on X , whose analytic index is the same as the topological signature of the … Wikipedia
Symmetric bilinear form — A symmetric bilinear form is, as the name implies, a bilinear form on a vector space that is symmetric. They are of great importance in the study of orthogonal polarities and quadrics.They are also more briefly referred to as symmetric forms when … Wikipedia
Metric signature — The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. That is, the corresponding real symmetric matrix is… … Wikipedia
Split-octonion — In mathematics, the split octonions are a nonassociative extension of the quaternions (or the split quaternions). They differ from the octonions in the signature of quadratic form: the split octonions have a split signature (4,4) whereas the… … Wikipedia
Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… … Wikipedia
Classification of Clifford algebras — In mathematics, in particular in the theory of nondegenerate quadratic forms on real and complex vector spaces, the finite dimensional Clifford algebras have been completely classified in terms of isomorphisms that preserve the Clifford product.… … Wikipedia
