The concept of the minimal polyanalytic polynomial was introduced by M. Huhtanen in connection with the generalized Lanczos process as applied to a normal matrix. The paper discusses the possibility of finding an equivalent of the characteristic polynomial in the set of polyanalytic polynomials.
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M. B. Balk and M. F. Zuev, “On polyanalytic functions,” Russ. Math. Surveys, 25, 201–223 (1970).
M. Huhtanen, “Orthogonal polyanalytic polynomials and normal matrices,” Math. Comp., 72, 355–373 (2002).
L. Elsner and Kh. D. Ikramov, “On a condensed form for normal matrices under finite sequences of elementary unitary similarities,” Linear Algebra Appl., 254, 79–98 (1997).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 463, 2017, pp. 154–159.
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Ikramov, K.D. The Minimal and Characteristic Polyanalytic Polynomials of a Normal Matrix. J Math Sci 232, 844–847 (2018). https://doi.org/10.1007/s10958-018-3914-x
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DOI: https://doi.org/10.1007/s10958-018-3914-x