Conjugate-normal matrices with conjugate-normal submatrices |
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Authors: | M Ghasemi Kamalvand Kh D Ikramov |
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Institution: | (1) Lorestan University, Khorramabad, Iran;(2) Moscow State University, Moscow, Russia |
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Abstract: | In studying the reduction of a complex n × n matrix A to its Hessenberg form by the Arnoldi algorithm, T. Huckle discovered
that an irreducible Hessenberg normal matrix with a normal leading principal m × m submatrix, where 1 < m < n, actually is
tridiagonal. We prove a similar assertion for the conjugate-normal matrices, which play the same role in the theory of unitary
congruences as the conventional normal matrices in the theory of unitary similarities. This fact is stated as a purely matrix-theoretic
theorem, without any reference to Arnoldi-like algorithms. Bibliography: 2 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 346, 2007, pp. 21–25. |
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