In mathematics, a Boolean 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. (In some contexts, particularly computer science, the term "Boolean matrix" implies this restriction.)
Let U be a non-trivial Boolean algebra (i.e. with at least two elements). Intersection, union, complementation, and containment of elements is expressed in U. Let V be the collection of n × n matrices that have entries taken from U. Complementation of such a matrix is obtained by complementing each element. The intersection or union of two such matrices is obtained by applying the operation to entries of each pair of elements to obtain the corresponding matrix intersection or union. A matrix is contained in another if each entry of the first is contained in the corresponding entry of the second.
The product of two Boolean matrices is expressed as follows:
According to one author, "Matrices over an arbitrary Boolean algebra β satisfy most of the properties over β0 = {0, 1}. The reason is that any Boolean algebra is a sub-Boolean algebra of for some set S, and we have an isomorphism from n × n matrices over "[1]
^Ki Hang Kim (1982) Boolean Matrix Theory and Applications, page 249, Appendix: Matrices over arbitrary Boolean Algebras, Marcel Dekker ISBN 0-8247-1788-0
mathematics, a Booleanmatrix is a matrix with entries from a Boolean algebra. When the two-element Boolean algebra is used, the Booleanmatrix is called a...
matrix, binary matrix, relation matrix, Booleanmatrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can...
Analysis of Boolean functions Balanced boolean function Bent function Boolean algebras canonically defined Boolean function BooleanmatrixBoolean-valued function...
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1...
51, Cambridge University Press ISBN 0-521-59916-4 Ki Hang Kim (1982) BooleanMatrix Theory and Applications, page 37, Marcel Dekker ISBN 0-8247-1788-0 Carlen...
ISSN 1572-9338. S2CID 254227100. Gunther Schmidt and Thomas Ströhlein (1976) "A Booleanmatrix iteration in timetable construction", Linear Algebra and Its Applications...
condition can be expressed using a Booleanmatrix. Use is made of the transpose of the Boolean localisation matrix L {\displaystyle \mathbf {L} } that...
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY...
may be applied include: computing the transitive closure of a graph, Booleanmatrix multiplication, edit distance calculation, sequence alignment, index...
reachable from node a. The data structure is typically stored as a Booleanmatrix, so if matrix[1][4] = true, then it is the case that node 1 can reach node...
parsing according to a general CFG is asymptotically equivalent to booleanmatrix multiplication (thus likely between quadratic and cubic time). One classical...
whether or not two vertices are connected (i.e., the connection matrix, which contains boolean values), it gives the exact distance between them. The convention...
A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned...
called the matrix semiring. Similarly, if R is a commutative semiring, then Mn(R) is a matrix semialgebra. For example, if R is the Boolean semiring (the...
{\displaystyle X=Y} ) form a matrix semiring (indeed, a matrix semialgebra over the Boolean semiring) where the identity matrix corresponds to the identity...
Procedures for MPOs)". Gunther Schmidt and Thomas Ströhlein (1976) "A Booleanmatrix iteration in timetable construction", Linear Algebra and Its Applications...
Laplacian matrix for the latter. In the matrix notation, the adjacency matrix of the undirected graph could, e.g., be defined as a Boolean sum of the...
d-or-fewer columns have the same boolean sum. A matrix is said to be d-disjunct if no set of d columns has a boolean sum which is a superset of any other...
equivalence with Booleanmatrix multiplication. They let A be the adjacency matrix of the given directed acyclic graph, and B be the adjacency matrix of its transitive...
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