Abstract
A linear parameterization of group GL(N, C) formed by certain basis of matrices with in advance known symmetry properties is offered. The concept of the canonical basis is introduced by means of direct product of the corresponding so-called generalized Gell-Mann matrices. The properties of this canonical basis are enumerated and proved; algorithm of finding inverse matrix order N in canonical basis is proposed.
Similar content being viewed by others
References
S. B. Pshenichnikov and R. M. Yamaleev, “Methods of Inverting Matrices of Order 2n,” Comput. Math. Math. Phys. 27(4), 188–191 (1987).
Kh. I. Semerdzhiev and R. M. Yamaleev, “Basis of Dickson Algebra and Its Matrix Realization,” Communication of JINR P5-88-834 (Dubna, 1988) [in Russian].
R. A. Bertlmann and Ph. Krammer, “Bloch Vectors for Qudits,” J. Phys. A: Math. Theor 41, 235303–235325 (2008).
F. I. Fedorov, Lorentz Group (Nauka, Moscow, 1979) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Lavrenov, A.N. Method of finding inverse matrix order N . Comput. Math. and Math. Phys. 52, 831–835 (2012). https://doi.org/10.1134/S0965542512060103
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542512060103