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

A.K. Abdikalykov; V.N. Chugunov; Kh.D. Ikramov

Special Matrices (2015)

- Volume: 3, Issue: 1, page 58-68, electronic only
- ISSN: 2300-7451

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topA.K. Abdikalykov, V.N. Chugunov, and Kh.D. Ikramov. "Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices." Special Matrices 3.1 (2015): 58-68, electronic only. <http://eudml.org/doc/270938>.

@article{A2015,

abstract = {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.},

author = {A.K. Abdikalykov, V.N. Chugunov, Kh.D. Ikramov},

journal = {Special Matrices},

keywords = {Toeplitz matrix; Hankel matrix; Toeplitz-plus-Hankel matrix; centrosymmetric matrix; skewcentrosymmetric
matrix; unitary similarity automorphism; skew-centrosymmetric matrix},

language = {eng},

number = {1},

pages = {58-68, electronic only},

title = {Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices},

url = {http://eudml.org/doc/270938},

volume = {3},

year = {2015},

}

TY - JOUR

AU - A.K. Abdikalykov

AU - V.N. Chugunov

AU - Kh.D. Ikramov

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

JO - Special Matrices

PY - 2015

VL - 3

IS - 1

SP - 58

EP - 68, electronic only

AB - 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.

LA - eng

KW - Toeplitz matrix; Hankel matrix; Toeplitz-plus-Hankel matrix; centrosymmetric matrix; skewcentrosymmetric
matrix; unitary similarity automorphism; skew-centrosymmetric matrix

UR - http://eudml.org/doc/270938

ER -

## References

top- [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] Zbl0739.65044
- [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] Zbl1306.15028
- [4] Kh.D. Ikramov, Unitary automorphisms of the space of Hankel matrices, Math. Notes 96(5) (2014) 678–685. [WoS] Zbl1315.15029
- [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. Zbl0839.15008
- [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). Zbl1318.15013
- [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.

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