Toeplitz-plus-Hankel circulants are reducible to block diagonal form via unitary congruences

Autor:	Khakim D. Ikramov
Rok vydání:	2014
Předmět:	Combinatorics Matrix (mathematics) Algebra and Number Theory Diagonal Block matrix Circulant matrix Centralizer and normalizer Physics::Atmospheric and Oceanic Physics Matrix similarity Toeplitz matrix Mathematics Cyclic permutation
Zdroj:	Linear and Multilinear Algebra. 63:862-867
ISSN:	1563-5139 0308-1087
DOI:	10.1080/03081087.2014.903571
Popis:	A Hankel circulant is a matrix obtained by reversing the order of columns (or rows) in a conventional circulant. A Toeplitz-plus-Hankel circulant (briefly, ()-circulant) is the sum of a circulant and a Hankel circulant. Bozzo discovered that the set of ()-circulants is the centralizer of the matrix , where is the cyclic permutation matrix. As a consequence, all the matrices in can be simultaneously brought to a block diagonal form with diagonal blocks of orders one and two by a unitary similarity transformation. We show that the same assertion holds for if unitary similarities are replaced by unitary congruences.
Databáze:	OpenAIRE
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