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Logical matrix

Index Logical matrix

A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0,1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. [1]

49 relations: Adjacency matrix, Analysis of variance, Binary relation, Bipartite graph, Block design, Boolean algebra, Boolean domain, Boolean satisfiability problem, Cardinality, Combinatorics, Composition of relations, Costas array, De Bruijn torus, Design matrix, Directed graph, Equality (mathematics), Expected value, Finite field, Finite geometry, Finite set, Go (game), Graph (discrete mathematics), Graph theory, Idempotence, Identity matrix, Incidence matrix, Inclusion (logic), Indexed family, Irving Copi, Journal of Symbolic Logic, Lattice (order), List of matrices, Logical conjunction, Logical disjunction, Loop (graph theory), Matrix (mathematics), Matrix multiplication, Modular arithmetic, Partially ordered set, Permutation matrix, Pixel, Prime-counting function, Quadratic sieve, Raster graphics, Redheffer matrix, Reflexive relation, Semiring, Smooth number, Square-free integer.

Adjacency matrix

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph.

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Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.

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Block design

In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application.

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Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

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Boolean domain

In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true.

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Boolean satisfiability problem

In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.

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In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

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Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Composition of relations

In the mathematics of binary relations, the composition relations is a concept of forming a new relation from two given relations R and S. The composition of relations is called relative multiplication in the calculus of relations.

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Costas array

In mathematics, a Costas array can be regarded geometrically as a set of n points lying on the squares of a n×n checkerboard, such that each row or column contains only one point, and that all of the n(n − 1)/2 displacement vectors between each pair of dots are distinct.

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De Bruijn torus

A De Bruijn torus. Each 2-by-2 binary matrix can be found within it exactly once. In combinatorial mathematics, a De Bruijn torus, named after Nicolaas Govert de Bruijn, is an array of symbols from an alphabet (often just 0 and 1) that contains every m-by-n matrix exactly once.

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Design matrix

In statistics, a design matrix, also known as model matrix or regressor matrix, is a matrix of values of explanatory variables of a set of objects, often denoted by X. Each row represents an individual object, with the successive columns corresponding to the variables and their specific values for that object.

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Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.

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Equality (mathematics)

In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

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Finite geometry

A finite geometry is any geometric system that has only a finite number of points.

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Finite set

In mathematics, a finite set is a set that has a finite number of elements.

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Go (game)

Go is an abstract strategy board game for two players, in which the aim is to surround more territory than the opponent.

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Graph (discrete mathematics)

In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.

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Identity matrix

In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.

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Incidence matrix

In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects.

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Inclusion (logic)

In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object.

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Indexed family

In mathematics, an indexed family is informally a collection of objects, each associated with an index from some index set.

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Irving Copi

Irving Marmer Copi (né Copilovich; July 28, 1917, Duluth, Minnesota – August 19, 2002, Honolulu, Hawaii) was an American philosopher, logician, and university textbook author.

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Journal of Symbolic Logic

The Journal of Symbolic Logic is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic.

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Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

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List of matrices

This page lists some important classes of matrices used in mathematics, science and engineering.

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Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

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Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

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Loop (graph theory)

In graph theory, a loop (also called a self-loop or a "buckle") is an edge that connects a vertex to itself.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Matrix multiplication

In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Permutation matrix


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In digital imaging, a pixel, pel, dots, or picture element is a physical point in a raster image, or the smallest addressable element in an all points addressable display device; so it is the smallest controllable element of a picture represented on the screen.

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Prime-counting function

In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by (x) (unrelated to the number pi).

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Quadratic sieve

The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve).

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Raster graphics

In computer graphics, a raster graphics or bitmap image is a dot matrix data structure that represents a generally rectangular grid of pixels (points of color), viewable via a monitor, paper, or other display medium.

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Redheffer matrix

In mathematics, a Redheffer matrix, studied by, is a (0,1) matrix whose entries aij are 1 if i divides j or if j.

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Reflexive relation

In mathematics, a binary relation R over a set X is reflexive if every element of X is related to itself.

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In abstract algebra, a semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.

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Smooth number

In number theory, a smooth (or friable) number is an integer which factors completely into small prime numbers.

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Square-free integer

In mathematics, a square-free integer is an integer which is divisible by no perfect square other than 1.

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(0,1) matrix, (0,1)-matrices, (0,1)-matrix, 0,1-matrix, 0-1 matrix, Binary matrix, Matrix logic, Zero-One matrix.


[1] https://en.wikipedia.org/wiki/Logical_matrix

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