Look up antisymmetric in Wiktionary, the free dictionary. Antisymmetric or skew-symmetric may refer to: Antisymmetry in linguistics Antisymmetry in physics...

binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle X} each...

In mathematics and theoretical physics, a tensor is antisymmetric or alternating on (or with respect to) an index subset if it alternates sign (+/−) when...

In Physics, antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction (DMI), is a contribution to the total magnetic exchange interaction...

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its...

names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of...

b} and b ≤ a {\displaystyle b\leq a} then a = b {\displaystyle a=b} (antisymmetric). a ≤ b {\displaystyle a\leq b} or b ≤ a {\displaystyle b\leq a} (strongly...

decomposed into a symmetric and an antisymmetric part. As the electromagnetic field is characterized by an antisymmetric rank-2 tensor, there is an obvious...

contraction with another set of indices when the expression is completely antisymmetric in each of the two sets of indices: A | α β γ | ⋯ B α β γ ⋯ = A α β...

are almost partial orders, but not quite, as they are not necessarily antisymmetric. A natural example of a preorder is the divides relation "x divides...

two identical particles, the total (many-particle) wave function is antisymmetric for fermions and symmetric for bosons. This means that if the space...

in V; alternating if B(v, v) = 0 for all v in V; skew-symmetric or antisymmetric if B(v, w) = −B(w, v) for all v, w in V; Proposition Every alternating...

combinations of properties. A partial order is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive...

{\displaystyle z\in V.} A complex skew-Hermitian form (also called an antisymmetric sesquilinear form), is a complex sesquilinear form s : V × V → C {\displaystyle...

words, more than one identical particle cannot occupy an antisymmetric state (one antisymmetric state can be occupied only by one particle). This is known...

of a symmetric matrix and an antisymmetric matrix. Applying this to the Jacobian matrix with symmetric and antisymmetric components E and R respectively:...

those that are symmetric, transitive, and antisymmetric, and those that are total, transitive, and antisymmetric. Pfeiffer has made some progress in this...

of a pseudoscalar is an antisymmetric (pure) tensor of order three. The Levi-Civita pseudotensor is a completely antisymmetric pseudotensor of order 3...

a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered...

[clarification needed] If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, total, trichotomous, a partial order, total...

parity (i.e. has an "even" or "positive" parity), and antisymmetric if the deuteron is antisymmetric under parity (i.e. has an "odd" or "negative" parity)...

relativity, the affine connection needed to be generalized to include an antisymmetric part, called the torsion. This modification was made by Einstein and...

elements, its nondegenerate molecular orbitals are either symmetric or antisymmetric with respect to any of these symmetries. In other words, the application...

Important examples of such tensors include symmetric and antisymmetric tensors. Antisymmetric tensors are commonly used to represent rotations (for example...

case for "is less than or equal to" and "preys on"). Symmetric and antisymmetric (where the only way a can be related to b and b be related to a is if...

Ψ2 is antisymmetric, Ψ3 is symmetric, and Ψ4 is antisymmetric with respect to the mirror plane. Similarly π is symmetric and π* is antisymmetric with respect...

(aRb\wedge bRa).} A relation is asymmetric if and only if it is both antisymmetric and irreflexive, so this may also be taken as a definition. An example...

for particles with half-integer spin (fermions), the wave function is antisymmetric under such an exchange. A consequence of the theorem is that non-interacting...

antisymmetrization converts any function in n {\displaystyle n} variables into an antisymmetric function. Let S {\displaystyle S} be a set and A {\displaystyle A} be...

mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the inverse of the result with unswapped...