Definition, Betydelse & Synonymer | Engelska ordet ANTISYMMETRIC

Definition av ANTISYMMETRIC

1. (linjär algebra, om en kvadratisk matris) skevsymmetrisk

Exempel på hur man kan använda ANTISYMMETRIC i en mening

• The divisibility relation on the natural numbers is an important example of an antisymmetric relation.
• In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative.
• Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations.
• However, there is a formula for finding the number of relations that are simultaneously reflexive, symmetric, and transitive – in other words, equivalence relations – , those that are symmetric and transitive, those that are symmetric, transitive, and antisymmetric, and those that are total, transitive, and antisymmetric.
• Technically, the Fock space is (the Hilbert space completion of) the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space ,.
• Absolute continuity of measures is reflexive and transitive, but is not antisymmetric, so it is a preorder rather than a partial order.
• Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped arguments.
• Because the bracket multiplication is antisymmetric, the Jacobi identity admits two equivalent reformulations.
• The minor relationship forms a partial order on the set of all distinct finite undirected graphs, as it obeys the three axioms of partial orders: it is reflexive (every graph is a minor of itself), transitive (a minor of a minor of G is itself a minor of G), and antisymmetric (if two graphs G and H are minors of each other, then they must be isomorphic).
• Fermions are particles whose wavefunction is antisymmetric, so under such a swap the wavefunction gets a minus sign, meaning that the amplitude for two identical fermions to occupy the same state must be zero.
• However, it is not satisfactory for fermions because the wave function above is not antisymmetric under exchange of any two of the fermions, as it must be according to the Pauli exclusion principle.
• Eisenschitz and London showed that this repulsion is a consequence of enforcing the electronic wavefunction to be antisymmetric under electron permutations.
• Einstein–Cartan theory relaxes this condition and, correspondingly, relaxes general relativity's assumption that the affine connection have a vanishing antisymmetric part (torsion tensor).
• Trivially, all scalars and vectors (tensors of order 0 and 1) are totally antisymmetric (as well as being totally symmetric).
• These functions are called the Schwinger functions (named after Julian Schwinger) and they are real-analytic, symmetric under the permutation of arguments (antisymmetric for fermionic fields), Euclidean covariant and satisfy a property known as reflection positivity.
• In (four-dimensional) Lorentzian spacetimes, there is a six-dimensional space of antisymmetric bivectors at each event.
• Because the vorticity tensor is antisymmetric, its diagonal components vanish, so it is automatically traceless (and we can replace it with a three-dimensional vector, although we shall not do this).
• The exterior bundle on M is the subbundle of the tensor bundle consisting of all antisymmetric covariant tensors.
• In VBT, wavefunctions are described as the sums and differences of VB determinants, which enforce the antisymmetric properties required by the Pauli exclusion principle.
• The same construct applies to any involutory function, such as the complex conjugate (real and imaginary parts), transpose (symmetric and antisymmetric matrices), and Hermitian adjoint (Hermitian and skew-Hermitian matrices).

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