Geodesic
The BMV-conjecture over quaternions and octonions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 6, pp. 185-222

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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. 
@article{FPM_2012_17_6_a5,
     author = {A. S. Smirnov},
     title = {The {BMV-conjecture} over quaternions and octonions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {185--222},
     publisher = {mathdoc},
     volume = {17},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_6_a5/}
}
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A. S. Smirnov. The BMV-conjecture over quaternions and octonions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 6, pp. 185-222. http://geodesic.mathdoc.fr/item/FPM_2012_17_6_a5/