Conjugate-normal matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 21-25
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In studying the reduction of a complex $n\times n$ matrix $A$ to its Hessenberg form by the Arnoldi algorithm, T. Huckle discovered that an irreducible Hessenberg normal matrix with a normal leading principal $m\times m$ submatrix, where $1, 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.
@article{ZNSL_2007_346_a1,
author = {M. Ghasemi Kamalvand and Kh. D. Ikramov},
title = {Conjugate-normal matrices},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {21--25},
year = {2007},
volume = {346},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a1/}
}
M. Ghasemi Kamalvand; Kh. D. Ikramov. Conjugate-normal matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 21-25. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a1/