Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T19:44:17.427Z Has data issue: false hasContentIssue false

Oppenheim's Inequality for the Second Immanant

Published online by Cambridge University Press:  20 November 2018

Russell Merris*
Affiliation:
Department of Mathematics and Computer Science California State University Hayward, CA 94542
Rights & Permissions [Opens in a new window]

Abstract

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.

Denote by d2 the immanant afforded by Sn and the character corresponding to the partition (2, 1n-2). If n ≥ 4, the following analog of Oppenheim's inequality is proved:

for all n-by-n positive semidefinite hermitian A and B.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Bapat, R.B. and Sunder, V.S., On majorization and Schur products, Linear Algebra Appl. 72 (1985), pp. 107117.Google Scholar
2. Chollet, J., Is there a permanental analogue to Oppenheim s inequality? Amer. Math. Monthly 89 (1982), pp. 5758.Google Scholar
3. Grone, R., An inequality for the second immanant, Linear and Multilinear Algebra 18 (1985), pp. 147152.Google Scholar
4. Grone, R. and Merris, R., A Fischer inequality for the second immanant, Linear Algebra Appl., 87 (1987), 77-83.Google Scholar
5. Marshall, A.W. and Olkin, I., Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979.Google Scholar
6. Merris, R., The second immanantal polynomial and the centroid of a graph, SIAM J. Algebraic and Discrete Methods, 7 (1986), 484-503.Google Scholar
7. Oppenheim, A., Inequalities connected with definite hermitian forms, J. London Math. Soc. 5 (1930), pp. 114119.Google Scholar