Logical matrix: Difference between revisions

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If ''m'' or ''n'' equals one, then the ''m'' × ''n'' logical matrix (M_{i j}) is a logical vector. If ''m'' = 1 the vector is a row vector, and if ''n'' = 1 it is a column vector. In either case the index equaling one is dropped from denotation of the vector.

Suppose <math>(P_i), \quad i = 1, 2,... m \ldots, \m</math> \text{and}\ \ <math>(Q_j), \quad j = 1, 2,... \ldots, n</math> are two logical vectors. The [[outer product]] of ''P'' and ''Q'' results in an ''m'' × ''n'' [[rectangular relation]]:

:<math>M_{i j} = P_i \land Q_j .</math> A re-ordering of the rows and columns of such a matrix can assemble all the ones into a rectangular part of the matrix.<ref name=GS>{{cite book | doi=10.1017/CBO9780511778810 | isbn=9780511778810 | author=Gunther Schmidt | page=91 | title=Relational Mathematics | chapter=6: Relations and Vectors | publisher=Cambridge University Press | year=2013 | author-link=Gunther Schmidt }}</ref>