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Term Rank of the Direct Product of Matrices

Published online by Cambridge University Press:  20 November 2018

Richard A. Brualdi
Richard A. Brualdi*
Affiliation:
University of Wisconsin, Madison, Wis.
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 126 - 138
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. MacDuffee, C. C., The theory of matrices, rev. ed. (New York, 1946).Google Scholar
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3. Ryser, H. J., Combinatorial mathematics, Carus Math. Monograph, no. 14 (New York, 1963).Google Scholar