Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices

• Autorzy: A.K. Abdikalykov , V.N. Chugunov , Kh.D. Ikramov
• Języki publikacji: EN

Abstrakty

EN

Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices. Generalizing this result, we give a complete description of unitary similarity automorphisms of the space of Toeplitz-plus-Hankel matrices.

Słowa kluczowe

EN

Toeplitz matrix; Hankel matrix; Toeplitz-plus-Hankel matrix; centrosymmetric matrix; skewcentrosymmetricmatrix; unitary similarity automorphism

Kategorie tematyczne

• 15B05: Toeplitz, Cauchy, and related matrices

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-03-10

zaakceptowano

2015-04-13

online

2015-04-20

Twórcy

autor

A.K. Abdikalykov

• Department of Mathematics, Kazakhstan Division of Moscow State University, Astana, Kazakhstan

autor

V.N. Chugunov

• Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation

autor

Kh.D. Ikramov

• Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russian Federation

Bibliografia

• [1] D.M. Wilkes, S.D. Morgera, F. Noor, M.H. Hayes, A Hermitian Toeplitz matrix is unitary similar to a real Toeplitz-plus-Hankel matrix, IEEE Trans. Signal Process. 39(9) (1991) 2146–2148. [Crossref]
• [2] A.K. Abdikalykov, Kh.D. Ikramov, V.N. Chugunov, Fast algorithms for calculating the eigenvalues of normal Toeplitzmatrices, Moscow Univ. Comput.Math. Cybernet. 38(1) (2014) 1–7. [Crossref]
• [3] Kh.D. Ikramov, Unitary automorphisms of the space of Toeplitz matrices, Dokl. Math. 89(3) (2014) 321–323. [WoS][Crossref]
• [4] Kh.D. Ikramov, Unitary automorphisms of the space of Hankel matrices, Math. Notes 96(5) (2014) 678–685. [WoS]
• [5] Kh.D. Ikramov, A.K. Abdikalykov, V.N. Chugunov, Unitary similarity automorphisms of the space of 3×3 Toeplitz-plus-Hankel matrices, Zap. Nauchn. Sem. S-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 428 (2014) 137–151.
• [6] A.K. Abdikalykov, Kh.D. Ikramov, V.N. Chugunov, Unitary similarity automorphisms of the space of 4×4 Toeplitz-plus-Hankel matrices, Moscow Univ. Comput.Math. Cybernet. 39(3) (2015) (in press).
• [7] R. Bevilacqua, N. Bonanni, E. Bozzi, On algebras of Toeplitz plus Hankel matrices, Linear Algebra Appl. 223/224 (1995) 99–118.
• [8] A.K. Abdikalykov, Centrosymmetric property of unitary matrices that preserve the set of (T+H)-matrices under similarity transformations, Comput. Math. Math. Phys. 55(4) (2015) (in press).
• [9] A.K. Abdikalykov, Unitary automorphisms of the space of (T +H)-matrices, Zap. Nauchn. Sem. S-Peterburg. Otdel.Mat. Inst. Steklov. (POMI) 428 (2014) 5–11.

Identyfikatory

DOI

10.1515/spma-2015-0006