Term Rank of the Direct Product of Matrices
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 126-138
Voir la notice de l'article provenant de la source Cambridge University Press
Let A = [aij] be a matrix of 0's and 1's or a (0, 1)-matrix of size m by m′. The term rank of A is denned as the maximal number of 1's of A with no two of the 1's on the same row or colunn. A theorem due to D. König (3, Theorem 5.1, p. 55) asserts that the term rank of A is also equal to the minimal number of rows and columns of A that collectively contain all the 1's. The term rank of A will be denoted by ρ(A). Obviously it is invariant under arbitrary permutations of the rows and columns of A. We assume without loss of generality that all matrices considered have no rows or columns consisting entirely of 0's.
Brualdi, Richard A. Term Rank of the Direct Product of Matrices. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 126-138. doi: 10.4153/CJM-1966-017-5
@article{10_4153_CJM_1966_017_5,
author = {Brualdi, Richard A.},
title = {Term {Rank} of the {Direct} {Product} of {Matrices}},
journal = {Canadian journal of mathematics},
pages = {126--138},
year = {1966},
volume = {18},
number = {1},
doi = {10.4153/CJM-1966-017-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-017-5/}
}
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