Geodesic
A Permanental Inequality—The Case of Equality
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1085-1090

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

In (3) we proved that if A is a complex n-square normal matrix with characteristic roots α1 ... , αn,then 1 If A is positive semi-definite hermitian, the inequality (1) becomes 2 This inequality partially answers the problem of determining the maximum permanent of a positive semi-definite hermitian matrix with prescribed characteristic roots (6). In (1), Brualdi and Newman proved that (2) also holds when A is an n-square circulant with non-negative entries. In a recent conversation Dr. Newman raised the question of determining the cases of equality in (1). In the present note we answer this question. 
Marcus, Marvin; Minc, Henryk. A Permanental Inequality—The Case of Equality. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1085-1090. doi: 10.4153/CJM-1966-108-x
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[1] 1. Brualdi, R. A. and Newman, M., Some theorems on the permanent (to appear). Google Scholar

[2] 2. Marcus, Marvin and Mine, Henryk, Inequalities for general matrix functions, Bull. Amer. Math. Soc., 70 (1964), 308–313. Google Scholar

[3] 3. Marcus, Marvin and Mine, Henryk, Generalized matrix functions, Trans. Amer. Math. Soc. (to appear). Google Scholar

[4] 4. Marcus, Marvin and Mine, Henryk, Permanents, Amer. Math. Monthly, 72 (1965), 577–591. Google Scholar

[5] 5. Marcus, Marvin and Mine, Henryk, A survey of matrix theory and matrix inequalities (Boston, Mass., 1964). Google Scholar

[6] 6. Marcus, Marvin and Newman, Morris, Inequalities for the permanent function, Ann. Math. (2), 75 (1962), 47–62. Google Scholar

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