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

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

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

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

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...

permuted, and the antisymmetrical class, in which for such a permutation the wave function changes its sign...[The antisymmetrical class is] the correct...

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

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...

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

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

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

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...

{\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...

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

symmetric and alternating squares are also known as the symmetric part and antisymmetric part of the tensor product. The second tensor power of a linear representation...

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...

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...

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

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

y is a blood relative of x. Antisymmetric for all x, y ∈ X, if xRy and yRx then x = y. For example, ≥ is an antisymmetric relation; so is >, but vacuously...

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

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

or alternatively as the exterior product to obtain a second order antisymmetric tensor x ∧ p. What does this combine with, if anything? There is another...

("plus") or an antisymmetric combination ("minus"). Particles that give symmetric combinations are called bosons; those with antisymmetric combinations...

equivalence relation. A partial order is a relation that is reflexive, antisymmetric, and transitive. Equality is both an equivalence relation and a partial...

subspace of T ( V ) {\displaystyle \mathrm {T} (V)} that consists of antisymmetric tensors. For characteristic 0 (or higher than ⁠ dim ⁡ V {\displaystyle...

of basis keep antisymmetric matrices antisymmetric, although strictly speaking, the quantity A(x,y) is not a matrix but an antisymmetric rank-two tensor...

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...