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In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other. More formally, is antisymmetric precisely if for all ,,, or equivalently, =.
Trivially, all scalars and vectors (tensors of order 0 and 1) are totally antisymmetric (as well as being totally symmetric). The electromagnetic tensor , F μ ν {\displaystyle F_{\mu \nu }} in electromagnetism .
That is, we assume that 1 + 1 ≠ 0, where 1 denotes the multiplicative identity and 0 the additive identity of the given field. If the characteristic of the field is 2, then a skew-symmetric matrix is the same thing as a symmetric matrix .
A skew-symmetric graph may equivalently be defined as the double covering graph of a polar graph or switch graph, [1] which is an undirected graph in which the edges incident to each vertex are partitioned into two subsets. Each vertex of the polar graph corresponds to two vertices of the skew-symmetric graph, and each edge of the polar graph ...
John- TOP nani-o what- ACC kaimashita bought ka Q John-wa nani-o kaimashita ka John-TOP what-ACC bought Q 'What did John buy' Japanese has an overt "question particle" (ka), which appears at the end of the sentence in questions. It is generally assumed that languages such as English have a "covert" (i.e. phonologically null) equivalent of this particle in the 'C' position of the clause — the ...
Formally, a binary relation R over a set X is symmetric if: [1], (), where the notation aRb means that (a, b) ∈ R. An example is the relation "is equal to", because if a = b is true then b = a is also true. If R T represents the converse of R, then R is symmetric if and only if R = R T. [2]
Antisymmetric or skew-symmetric may refer to: . Antisymmetry in linguistics; Antisymmetry in physics; Antisymmetric relation in mathematics; Skew-symmetric graph; Self-complementary graph
There are many examples of symmetric tensors. Some include, the metric tensor, , the Einstein tensor, and the Ricci tensor, .. Many material properties and fields used in physics and engineering can be represented as symmetric tensor fields; for example: stress, strain, and anisotropic conductivity.