Definition, Betydelse & Synonymer | Engelska ordet SKEW-SYMMETRIC

Definition av SKEW-SYMMETRIC

1. (linjär algebra) skevsymmetrisk

Exempel på hur man kan använda SKEW-SYMMETRIC i en mening

• At the level of forms, this can be seen by decomposing a Hermitian form into its real and imaginary parts: the real part is symmetric (orthogonal), and the imaginary part is skew-symmetric (symplectic)—and these are related by the complex structure (which is the compatibility).
• In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative.
• It is straightforward to verify that the above definition is bilinear, and is skew-symmetric; one can also show that it obeys the Jacobi identity.
• There is also a structure theorem for Gorenstein rings of codimension 3 in terms of the Pfaffians of a skew-symmetric matrix, by Buchsbaum and Eisenbud.
• The convention on skew-symmetric tridiagonal matrices, given below in the examples, then determines one specific polynomial, called the Pfaffian polynomial.
• Note that A is skew-symmetric (respectively, skew-Hermitian) if and only if Q is orthogonal (respectively, unitary) with no eigenvalue −1.
• The Laplace–de Rham operator differs more significantly from the tensor Laplacian restricted to act on skew-symmetric tensors.
• Bivector § Tensors and matrices (but note that the stress–energy tensor is symmetric, not skew-symmetric).
• Conversely, singly even-dimensional manifolds have a skew-symmetric nondegenerate bilinear form on their middle dimension; if one defines a quadratic refinement of this to a quadratic form (as on a framed manifold), one obtains the Arf invariant as a mod 2 invariant.
• The symmetrization and antisymmetrization of a bilinear map are bilinear; thus away from 2, every bilinear form is a sum of a symmetric form and a skew-symmetric form, and there is no difference between a symmetric form and a quadratic form.
• For planar graphs (regardless of bipartiteness), the FKT algorithm computes the number of perfect matchings in polynomial time by changing the signs of a carefully chosen subset of the entries in the Tutte matrix of the graph, so that the Pfaffian of the resulting skew-symmetric matrix (the square root of its determinant) is the number of perfect matchings.
• De Klerk, Etienne; Roos, Cornelis; Terlaky, Tamás (1997) “Initialization in semidefinite programming via a self-dual skew-symmetric embedding” Operations Research Letters 20 (5), 213-221.

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