No CrossRef data available.
Article contents
Multilinear Functions of Row Stochastic Matrices
Published online by Cambridge University Press: 20 November 2018
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.
In the study of inequalities, the cases of equality are often the most difficult and interesting part. The case of equality is, in some sense, a measure of the tightness of the inequality. In this paper, we generalize two inequalities of Brualdi and Newman [1, Theorems 3, 4], but the instances of equality are probably more interesting because of the variety of cases which can occur.
Let A = (aij) be an n × n matrix. Define the permanent of A by
We say that A is row stochastic if all entries are non-negative and all row sums are 1. In [1], several inequalities involving permanents of row stochastic matrices were proved. In two of these results, the case of equality was not determined. We will generalize both of these results to a class of functions which includes the permanent, and determine all cases of equality.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1971
Footnotes
This work was partially supported by NRC Grant A7862.
References
1.
Brualdi, R. A. and Newman, M., Inequalities for the permanental minors of non-negative matrices, Can. J. Math.
18 (1966), 608–615.Google Scholar
2.
Marcus, M. and Pierce, S., On a combinatorial result of Brualdi and Newman, Can. J. Math.
20 (1968), 1056–1067.Google Scholar
3.
Marcus, M. and Soüles, G., Inequalities for combinatorial matrix functions, J. Combinatorial Theory. (1967), 145–163.Google Scholar
You have
Access