Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T04:03:33.266Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
2. Ore, O., Graphs and matching theorems, Duke Math. J., 22 (1955), 625–639.Google Scholar
3. Ryser, H. J., Combinatorial mathematics, Carus Math. Monograph, no. 14 (New York, 1963).Google Scholar