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Logical matrix information


A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in combinatorial mathematics and theoretical computer science.

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Logical matrix

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A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a...

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Transpose

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case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT. The transpose of a matrix A, denoted...

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Incidence matrix

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

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Outer product

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a logical vector, a special case of a logical matrix. The logical operation and takes the place of multiplication. The outer product of two logical vectors...

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Binary relation

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The logical matrix of C is the outer product of logical vectors C i j   =   u i v j , u , v {\displaystyle C_{ij}\ =\ u_{i}v_{j},\quad u,v} logical vectors...

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Exclusive or

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disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs...

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List of named matrices

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matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

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Boolean matrix

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matrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Boolean matrix is called a logical matrix....

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Algebraic logic

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relation may be represented by a logical matrix; then the converse relation is represented by the transpose matrix. A relation obtained as the composition...

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Logical clock

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A logical clock is a mechanism for capturing chronological and causal relationships in a distributed system. Often, distributed systems may have no physically...

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List of Matrix series characters

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This is a list of characters from The Matrix franchise universe. Many of the characters listed here have names reflecting certain aspects of them, such...

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List of Boolean algebra topics

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Boolean matrix Boolean-valued function Conditioned disjunction Evasive Boolean function Exclusive or Functional completeness Logical biconditional Logical conjunction...

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Laplacian matrix

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theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a...

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Ansoff matrix

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stakeholders.[citation needed] The logic of the Ansoff matrix has been questioned. The logical issues pertain to interpretations about newness. If one...

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Directed graph

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i. The adjacency matrix of a directed graph is a logical matrix, and is unique up to permutation of rows and columns. Another matrix representation for...

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Truth table

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"The Philosophy of Logical Atomism" truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication...

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Homogeneous relation

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to a logical matrix of 0s and 1s, where the expression xRy corresponds to an edge between x and y in the graph, and to a 1 in the square matrix of R....

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Converse relation

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X:(x,y)\in L\}.} Since a relation may be represented by a logical matrix, and the logical matrix of the converse relation is the transpose of the original...

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The Matrix

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The Matrix is a 1999 science fiction action film written and directed by the Wachowskis. It is the first installment in the Matrix film series, starring...

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Bit array

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represented by a bit array called a logical matrix. In the calculus of relations, these arrays are composed with matrix multiplication where the arithmetic...

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Composition of relations

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the matrix product of two logical matrices will be 1, then, only if the row and column multiplied have a corresponding 1. Thus the logical matrix of a...

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Zhegalkin polynomial

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\\c_{2}\\c_{3}\\c_{4}\\c_{5}\\c_{6}\\c_{7}\end{pmatrix}}} by an 8x8 logical matrix which represents the possible values that all the possible conjunctions...

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History of type theory

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generalized) notion of "matrix", that of a "logical matrix . . . one that contains no constants. Thus p|q is a logical matrix". Thus Russell has virtually...

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Logical biconditional

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mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used...

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Sparse matrix

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In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict...

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Partially ordered set

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(ker), and converse relation (cnv). Each relation is depicted by its logical matrix for the poset whose Hasse diagram is depicted in the center. For example...

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Outline of logic

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Functional completeness Implicant Logic alphabet Logic redundancy Logical connective Logical matrix Product term True quantified Boolean formula Truth table Predicate...

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Jacques Riguet

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the logical matrix associated with a relation. If u and v are logical vectors, then their logical outer product produces the associated logical matrix u...

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