An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices-Reference-Cited by-同舟云学术

An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices

Published:2021-01-01 Issue:1 Volume:9 Page:83-102
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Hutchinson George¹

Affiliation:

1. Department of Mathematical Sciences , Lakehead University , Thunder Bay, Ontario, P7B 5E1 , Canada

Abstract

Abstract A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2020-0126/pdf

Reference8 articles.

1. [1] J. Chollet. Is there a permanental analogue to Oppenheim’s inequality? The Amer. Math. Monthly, 89(1):57–58, 1982.

2. [2] A. Oppenheim. Inequalities connected with definite Hermitian forms. J. Lond. Math. Soc., 1(2): 114–119, 1930

3. [3] R. J. Gregorac and I.R. Hentzel. A note on the analogue of Oppenheim’s inequality for permanents. Linear Algebra Appl., 94: 109–112, 1987.

4. [4] R. B. Bapat and V. S. Sunder On majorization and Schur products. Linear Algebra Appl., 72: 107–117, 1985.

5. [5] S. Drury. A counterexample to a question of Bapat and Sunder. Electron. J. Linear Algebra, 31: 69–70, 2016.

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