Simultaneous reduction to block
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 49-62
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Analogs of some classical theorems on commuting matrices are proved. The new theorems deal with unitary congruences rather than unitary similarities; commutation is replaced by concommutation, defined in the paper, whereas normal and Hermitian matrices are replaced by conjugate-normal and symmetric matrices, respectively.
@article{ZNSL_2007_346_a4,
author = {Kh. D. Ikramov and H. Fassbender},
title = {Simultaneous reduction to block},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {49--62},
year = {2007},
volume = {346},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a4/}
}
Kh. D. Ikramov; H. Fassbender. Simultaneous reduction to block. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XX, Tome 346 (2007), pp. 49-62. http://geodesic.mathdoc.fr/item/ZNSL_2007_346_a4/
[1] M. Markus, Kh. Mink, Obzor po teorii matrits i matrichnykh neravenstv, Nauka, M., 1972 | MR
[2] Y. P. Hong, R. A. Horn, “On simultaneous reduction of families of matrices to triangular or diagonal form by unitary congruences”, Linear Multilinear Algebra, 17 (1985), 271–288 | DOI | MR | Zbl
[3] H. Fassbender, Kh. D. Ikramov, “Some observations on the Youla form and conjugate-normal matrices”, Linear Algebra Appl., 422 (2007), 29–38 | DOI | MR | Zbl
[4] R. Khorn, Ch. Dzhonson, Matrichnyi analiz, Mir, M., 1990 | MR
[5] D. C. Youla, “A normal form for a matrix under the unitary congruence group”, Canad. J. Math., 13 (1961), 694–704 | DOI | MR | Zbl