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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 207–218 (Mi mz4033)  

This article is cited in 6 scientific papers (total in 6 papers)

On Normal Hankel Matrices of Low Orders

Kh. D. Ikramova, V. N. Chugunovb

a M. V. Lomonosov Moscow State University
b Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: In the previous work of the authors, the problem of describing complex $n\times n$ matrices that are simultaneously normal and Hankel was reduced to a system of $n-1$ real equations with respect to $2n$ unknowns. These equations are quadratic, and it is not at all clear whether they have real solutions. It is shown here that the systems corresponding to $n=3$ and $n=4$ are solvable and have infinitely many real solutions.

Keywords: Hankel matrix, normal matrix, Toeplitz matrix, backward identity, circulant, Hankel circulant, upper (lower) triangular matrix, Cramer's rule

DOI: https://doi.org/10.4213/mzm4033

Full text: PDF file (480 kB)
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English version:
Mathematical Notes, 2008, 84:2, 197–206

Bibliographic databases:

UDC: 517.958
Received: 20.07.2007

Citation: Kh. D. Ikramov, V. N. Chugunov, “On Normal Hankel Matrices of Low Orders”, Mat. Zametki, 84:2 (2008), 207–218; Math. Notes, 84:2 (2008), 197–206

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kh. D. Ikramov, V. N. Chugunov, “On the Reduction of the Normal Hankel Problem to Two Particular Cases”, Math. Notes, 85:5 (2009), 674–681  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. N. Chugunov, “On two particular cases of solving the normal Hankel problem”, Comput. Math. Math. Phys., 49:6 (2009), 893–900  mathnet  crossref  zmath  isi
    3. Ikramov Kh. D., Chugunov V. N., “Classifying normal Hankel matrices”, Dokl. Math., 79:1 (2009), 114–117  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    4. Mei Y., “The Inverse Matrices of Symmetric Circulant Hankel Matrices Constituted by Equal Ratio”, Proceedings of the Third International Workshop on Applied Matrix Theory, eds. Xu C., Xu G., Zhang F., World Acad Union-World Acad Press, 2009, 262–264  mathscinet  isi
    5. V. N. Chugunov, “On particular solutions of the normal $T+H$-problem”, Comput. Math. Math. Phys., 50:4 (2010), 583–588  mathnet  crossref  mathscinet  adsnasa  isi
    6. Chugunov V.N., Ikramov Kh.D., “A complete solution of the normal Hankel problem”, Linear Algebra Appl., 432:12 (2010), 3210–3230  crossref  mathscinet  zmath  isi  elib  scopus
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