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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 16, 2015

Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices

  • Jesús Gutiérrez-Gutiérrez EMAIL logo and Marta Zárraga-Rodríguez
From the journal Special Matrices

Abstract

In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.

References

[1] J. Gutiérrez-Gutiérrez, Powers of real persymmetric anti-tridiagonal matrices with constant anti-diagonals, Applied Mathematics and Computation 206 (2008) 919-924.10.1016/j.amc.2008.10.003Search in Google Scholar

[2] J. Gutiérrez-Gutiérrez, Eigenvalue decomposition for persymmetric Hankel matrices with at most three non-zero anti-diagonals, Applied Mathematics and Computation 234 (2014) 333-338.10.1016/j.amc.2014.01.169Search in Google Scholar

[3] M. Akbulak, C. M. da Fonseca, F. Yılmaz, The eigenvalues of a family of persymmetric anti-tridiagonal 2-Hankel matrices, Applied Mathematics and Computation 225 (2013) 352-357.10.1016/j.amc.2013.09.014Search in Google Scholar

[4] J. Rimas, On computing of arbitrary integer powers of even order anti-tridiagonal matrices with zeros in main skew diagonal and elements 1, 1, 1, ..., 1; −1, −1, −1, ..., −1 in neighbouring diagonals, Applied Mathematics and Computation 204 (2008) 754-763.10.1016/j.amc.2008.07.021Search in Google Scholar

[5] J. Rimas, On computing of arbitrary positive integer powers of odd order anti-tridiagonal matrices with zeros in main skew diagonal and elements 1, 1, 1, ..., 1; −1, −1, −1, ..., −1 in neighbouring diagonals, Applied Mathematics and Computation 210 (2009) 64-71.10.1016/j.amc.2008.11.001Search in Google Scholar

[6] C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.10.1137/1.9780898719512Search in Google Scholar

[7] P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic Press, 1985.Search in Google Scholar

[8] J. Gutiérrez-Gutiérrez, Powers of complex persymmetric or skew-persymmetric anti-tridiagonal matrices with constant anti-diagonals, Applied Mathematics and Computation 217 (2011) 6125-6132.10.1016/j.amc.2010.12.091Search in Google Scholar

[9] J. Lita da Silva, Integer powers of anti-tridiagonal matrices of the form antitridiagn (a, c, −a), a, c ∈ ℂ, International Journal of Computer Mathematics (2015) DOI: 10.1080/00207160.2015.1073721.10.1080/00207160.2015.1073721Search in Google Scholar

[10] J. Gutiérrez-Gutiérrez, Powers of tridiagonal matrices with constant diagonals, Applied Mathematics and Computation 206 (2008) 885-891.10.1016/j.amc.2008.10.005Search in Google Scholar

[11] T. M. Apostol, Calculus, Vol. 1, John Wiley & Sons, 1967.Search in Google Scholar

Received: 2015-5-13
Accepted: 2015-11-12
Published Online: 2015-12-16
Published in Print: 2016-1-1

© 2016 Jesús Gutiérrez-Gutiérrez et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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