Geodesic
Hamiltonian square roots of skew Hamiltonian quaternionic matrices
The electronic journal of linear algebra, Tome 17 (2008), pp. 168-191.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Criteria for existence of Hamiltonian quaternionic matrices that are square roots of a given skewHamiltonian quaternionic matrix are developed. The criteria are formulated in terms of respective canonical forms of skewHamiltonian quaternionic matrices. The Hamiltonian property is understood with respect to either the quaternionic conjugation, or an involutory antiautomorphism of the quaternions which is different from the quaternionic conjugation. Many results are stated and proved in a more general framework of symmetric and skewsymmetric matrices with respect to an invertible matrix which is skewsymmetric relative to an involutory antiautomorphism.
Classification : 15A21, 15A33
Keywords: Hamiltonian matrix, skewhamiltonian matrix, quaternion, square root 
@article{ELA_2008__17__a31,
     author = {Rodman, Leiba},
     title = {Hamiltonian square roots of skew {Hamiltonian} quaternionic matrices},
     journal = {The electronic journal of linear algebra},
     pages = {168--191},
     publisher = {mathdoc},
     volume = {17},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2008__17__a31/}
}
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Rodman, Leiba. Hamiltonian square roots of skew Hamiltonian quaternionic matrices. The electronic journal of linear algebra, Tome 17 (2008), pp. 168-191. http://geodesic.mathdoc.fr/item/ELA_2008__17__a31/