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A binary opposition (also binary system) is a pair of related terms or concepts that are opposite in meaning. Binary opposition is the system of language and/or thought by which two theoretical opposites are strictly defined and set off against one another. [ 1 ]
When modelling relations between two different classes of objects, bipartite graphs very often arise naturally. For instance, a graph of football players and clubs, with an edge between a player and a club if the player has played for that club, is a natural example of an affiliation network, a type of bipartite graph used in social network analysis.
In group theory, a branch of mathematics, an opposite group is a way to construct a group from another group that allows one to define right action as a special case of left action. Monoids , groups, rings , and algebras can be viewed as categories with a single object.
A permutation matrix is a (0, 1)-matrix, all of whose columns and rows each have exactly one nonzero element.. A Costas array is a special case of a permutation matrix.; An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between points (or vertices) and lines of a geometry, blocks of a block design, or edges of a graph.
Used to form compound adjectives such as lineo-linear, lineo-quadric, and so on, indicating the bidegree of something. For example, lineo-linear means having degree 1 in each of two sets of variables. In particular the lineo-linear invariant of two binary forms has degree 1 in the coefficients of each form. (Elliott 1895, p.54) Lüroth invariant
A binary operation ∗ on the set S is associative when this diagram commutes. That is, when the two paths from S×S×S to S compose to the same function from S×S×S to S. Formally, a binary operation on a set S is called associative if it satisfies the associative law:
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
In mathematics, the signature (v, p, r) [clarification needed] of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix g ab of the metric tensor with respect to a basis.
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