Look up antisymmetric in Wiktionary, the free dictionary.
Antisymmetric or skew-symmetric may refer to:
Antisymmetry in linguistics
Antisymmetry in physics
Antisymmetric relation in mathematics
Skew-symmetric graph
Self-complementary graph
In mathematics, especially linear algebra, and in theoretical physics, the adjective antisymmetric (or skew-symmetric) is used for matrices, tensors, and other objects that change sign if an appropriate operation (e.g. matrix transposition) is performed. See:
Skew-symmetric matrix (a matrix A for which AT = −A)
Skew-symmetric bilinear form is a bilinear form B such that B(x, y) = −B(y, x) for all x and y.
Antisymmetric tensor in matrices and index subsets.
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...
Look up antisymmetric in Wiktionary, the free dictionary. Antisymmetric or skew-symmetric may refer to: Antisymmetry in linguistics Antisymmetry in physics...
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...
In Physics, antisymmetric exchange, also known as the Dzyaloshinskii–Moriya interaction (DMI), is a contribution to the total magnetic exchange interaction...
permuted, and the antisymmetrical class, in which for such a permutation the wave function changes its sign...[The antisymmetrical class is] the correct...
words, more than one identical particle cannot occupy an antisymmetric state (one antisymmetric state can be occupied only by one particle). This is known...
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...
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...
those that are symmetric, transitive, and antisymmetric, and those that are total, transitive, and antisymmetric. Pfeiffer has made some progress in this...
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...
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...
('plus') or an antisymmetric combination ('minus'). Particles that give symmetric combinations are called bosons; those with antisymmetric combinations...
{\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...
a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered...
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...
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...
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...
isotropic exchange would align the spins exactly antiparallel, while antisymmetric exchange arising from relativistic effects (spin–orbit coupling) would...
{\displaystyle Y} . If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, total, trichotomous, a partial order, total...
{\displaystyle R\cup R^{\operatorname {T} }} is left (or right) quasi-reflexive. antisymmetric if whenever x , y ∈ X {\displaystyle x,y\in X} are such that x R y and ...
{\displaystyle V} be a real vector space equipped with a nonsingular real antisymmetric bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} (i.e. a symplectic...
parity (i.e. have an "even" or "positive" parity), and antisymmetric if the deuteron is antisymmetric under parity (i.e. have an "odd" or "negative" parity)...
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...
symmetric, but not necessarily antisymmetric, is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively. All definitions...
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