The decomplexification technique proposed for coneigenvalue problems in a recent paper by T. Jiang et al. is discussed and compared with the classical decomplexification technique for eigenvalue problems. Simple explanations for both techniques are presented, and their properties concerning special matrix classes are indicated. Bibliography: 4 titles.
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Kh. D. Ikramov, Linear Algebra. Problem Book [in Russian], Mir, Moscow (1983).
T. Jiang, X. Cheng, and L. Chen, “An algebraic relation between consimilarity and similarity of complex matrices and its applications,” J. Phys. A: Math. Gen., 39, 9215–9222 (2006).
Kh. D. Ikramov, “On the coneigenvalues and singular values of a complex square matrix,” Zap. Nauchn. Semin. POMI, 334, 111–120 (2006).
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1989).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 36–41.
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Ikramov, K.D. Decomplexification of eigenvalue and coneigenvalue problems. J Math Sci 157, 692–694 (2009). https://doi.org/10.1007/s10958-009-9350-1
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DOI: https://doi.org/10.1007/s10958-009-9350-1