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# Logical matrix

A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0,1) matrix is a matrix with entries from the Boolean domain B. [1]

In mathematics, computer science and application areas such as sociology, an adjacency matrix is a means of representing which vertices (or nodes) of a graph are adjacent to which other vertices.

## Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences among group means and their associated procedures (such as "variation" among and between groups), developed by statistician and evolutionary biologist Ronald Fisher.

## Binary relation

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

## 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 sets U and V (that is, U and V are each independent sets) such that every edge connects a vertex in U to one in V. Vertex set U and V are often denoted as partite sets.

## 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.

## Boolean domain

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

## 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.

## Cardinality

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

## Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

## Composition of relations

In mathematics, the composition of binary relations is a concept of forming a new relation from two given relations R and S, having as its most well-known special case the composition of functions.

## Costas array

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

## 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.

## Design matrix

In statistics, a design matrix is a matrix of values of explanatory variables, often denoted by X, that is used in certain statistical models, e.g., the general linear model.

## 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.

## 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.

## Finite geometry

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

## Finite set

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

## Graph (mathematics)

In mathematics, and more specifically in graph theory, a graph is a representation of a set of objects where some pairs of objects are connected by links.

## Graph theory

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

## Idempotence

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

## Identity matrix

In linear algebra, the identity matrix or unit matrix of size n is the n &times; n square matrix with ones on the main diagonal and zeros elsewhere.

## Incidence matrix

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

## Indexed family

In mathematics, an indexed family is a collection of values associated with indices.

## List of matrices

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

## Logical conjunction

In logic and mathematics, 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.

## 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.

## Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is interpreted and manipulated in certain prescribed ways.

## Matrix multiplication

In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix.

## Modular arithmetic

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

## Permutation matrix

In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere.

## Pixel

In digital imaging, a pixel, pel, 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.

## 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 \scriptstyle\pi(x) (unrelated to the number pi).

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

## Raster graphics

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

## 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.

## Relation algebra

In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.

## Semiring

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.

## Smooth number

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

## Square-free integer

In mathematics, a square-free, or quadratfrei (from German language) integer, is an integer which is divisible by no other perfect square than 1.

## Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

## References

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