Geodesic
Multilinear Functions of Row Stochastic Matrices
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 833-843

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Pierce, Stephen. Multilinear Functions of Row Stochastic Matrices. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 833-843. doi: 10.4153/CJM-1971-092-7
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[1] 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] 2. Marcus, M. and Pierce, S., On a combinatorial result of Brualdi and Newman, Can. J. Math. 20 (1968), 1056–1067. Google Scholar

[3] 3. Marcus, M. and Soüles, G., Inequalities for combinatorial matrix functions, J. Combinatorial Theory. (1967), 145–163. Google Scholar

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