FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 6, PAGES 185-222

The BMV-conjecture over quaternions and octonions

A. S. Smirnov

Abstract

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This paper investigates generalizations of the BMV-conjecture for quaternionic and octonionic matrices. For quaternions the correctness of the formulation is shown as well as its equivalence to the original conjecture for complex matrices. General properties of octonions and Hermitian matrices over them are examined for the BMV-conjecture formulation over octonions.

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Last modified: November 21, 2012