Logical matrix: Difference between revisions

Revision as of 21:33, 13 January 2022

Revision as of 21:36, 13 January 2022

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==Other examples==

* 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 (discrete mathematics)]].

* A [[design matrix]] in [[analysis of variance]] is a (0, 1)-matrix with constant row sums.

* A logical matrix may represent an [[adjacency matrix]] in [[graph theory]]: non-symmetric matrices correspond to [[directed graph]]s, symmetric matrices to ordinary [[graph (discrete mathematics)|graph]]s, and a 1 on the diagonal corresponds to a [[loop (graph theory)|loop]] at the corresponding vertex.

* The [[biadjacency matrix]] of a simple, undirected [[bipartite graph]] is a (0, 1)-matrix, and any (0, 1)-matrix arises in this way.

* The prime factors of a list of ''m'' [[square-free integer|square-free]], [[smooth number|''n''-smooth]] numbers can be described as a ''m''&timesnbsp;× π(''n'') (0, 1)-matrix, where π is the [[prime-counting function]], and ''a''_''ij'' is 1 if and only if the ''j''th prime divides the ''i''th number. This representation is useful in the [[quadratic sieve]] factoring algorithm.

* A [[Raster graphics|bitmap image]] containing [[pixel]]s in only two colors can be represented as a (0, 1)-matrix in which the 0'szeros represent pixels of one color and the 1'sones represent pixels of the other color.

* A binary matrix can be used to check the game rules in the game of [[Go (game)|Go]]<ref>{{cite web |url=http://senseis.xmp.net/?BinMatrix |title=Binmatrix |date=February 8, 2013 |access-date=August 11, 2017 |first=Kjeld |last=Petersen}}</ref>

==Some properties==