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

Jesús Gutiérrez-Gutiérrez; Marta Zárraga-Rodríguez

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 73-79
  • ISSN: 2300-7451

Abstract

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

How to cite

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Jesús Gutiérrez-Gutiérrez, and Marta Zárraga-Rodríguez. "Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices." Special Matrices 4.1 (2016): 73-79. <http://eudml.org/doc/276940>.

@article{JesúsGutiérrez2016,
abstract = {In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.},
author = {Jesús Gutiérrez-Gutiérrez, Marta Zárraga-Rodríguez},
journal = {Special Matrices},
keywords = {Anti-tridiagonal matrices; Hankel matrices; orthogonal diagonalization; skew-persymmetric matrices; anti-tridiagonal matrices},
language = {eng},
number = {1},
pages = {73-79},
title = {Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices},
url = {http://eudml.org/doc/276940},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Jesús Gutiérrez-Gutiérrez
AU - Marta Zárraga-Rodríguez
TI - Orthogonal diagonalization for complex skew-persymmetric anti-tridiagonal Hankel matrices
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 73
EP - 79
AB - In this paper, we obtain an eigenvalue decomposition for any complex skew-persymmetric anti-tridiagonal Hankel matrix where the eigenvector matrix is orthogonal.
LA - eng
KW - Anti-tridiagonal matrices; Hankel matrices; orthogonal diagonalization; skew-persymmetric matrices; anti-tridiagonal matrices
UR - http://eudml.org/doc/276940
ER -

References

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  1. [1] J. Gutiérrez-Gutiérrez, Powers of real persymmetric anti-tridiagonal matrices with constant anti-diagonals, Applied Mathematics and Computation 206 (2008) 919-924.[WoS] Zbl1158.15026
  2. [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.[WoS] Zbl1298.15039
  3. [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.[WoS] Zbl1334.15071
  4. [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.[WoS] Zbl1154.65001
  5. [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.[WoS] Zbl1162.65336
  6. [6] C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.[WoS] 
  7. [7] P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic Press, 1985. Zbl0558.15001
  8. [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.[WoS] Zbl1220.15020
  9. [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.[Crossref] 
  10. [10] J. Gutiérrez-Gutiérrez, Powers of tridiagonal matrices with constant diagonals, Applied Mathematics and Computation 206 (2008) 885-891.[WoS] Zbl1158.15025
  11. [11] T. M. Apostol, Calculus, Vol. 1, John Wiley & Sons, 1967. 

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