Further results on generalized centro-invertible matrices

  • Leila Lebtahi
  • Óscar Romero
  • Néstor Thome
Original Paper


This paper deals with generalized centro-invertible matrices introduced by the authors in Lebtahi et al. (Appl. Math. Lett. 38, 106–109, 2014). As a first result, we state the coordinability between the classes of involutory matrices, generalized centro-invertible matrices, and {K}-centrosymmetric matrices. Then, some characterizations of generalized centro-invertible matrices are obtained. A spectral study of generalized centro-invertible matrices is given. In addition, we prove that the sign of a generalized centro-invertible matrix is {K}-centrosymmetric and that the class of generalized centro-invertible matrices is closed under the matrix sign function. Finally, some algorithms have been developed for the construction of generalized centro-invertible matrices.


Centrosymmetric matrices Centro-invertible matrices Spectral analysis Inverse problem Matrix sign function 

Mathematics Subject Classification (2010)

15A09 15A18 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Funding information

This paper was partially supported by Ministerio de Economía y Competitividad of Spain (Grant number DGI MTM2013-43678-P and Grant Red de Excelencia MTM2017-90682-REDT).


  1. 1.
    Abu-Jeib, I.: Centrosymmetric matrices: properties and an alternative approach. Can. Appl. Math. Q. 10(4), 429–445 (2002)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Bai, Z.: The inverse eigenproblem of centrosymmetric matrices with a submatrix constraint and its approximation. SIAM J. Matrix Anal. Appl. 26(4), 1100–1114 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ben-Israel, A., Greville, T.: Generalized inverses: theory and applications, Wiley, 2nd edn. (2003)Google Scholar
  4. 4.
    Cantoni, A., Butler, P.: Eigenvalues and eigenvectors of symmetric centrosymmetrlc matrices. Linear Algebra Appl. 13, 275–288 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    El-Mikkawy, M., Atlan, F.: On solving centrosymmetric linear systems. Appl. Math. 4, 21–32 (2013)CrossRefzbMATHGoogle Scholar
  6. 6.
    Gaudreau, P., Safouhi, H.: Centrosymmetric matrices in the sinc collocation method for Sturm-Liouville problems. EPJ Web of Conferences 108(0), 2016 (1004). Google Scholar
  7. 7.
    Higham, N.: Function of matrices: theory and computation. SIAM (2008)Google Scholar
  8. 8.
    Lebtahi, L., Romero, O., Thome, N.: Characterizations of {K,s + 1}-potent matrices and applications. Linear Algebra Appl. 436, 293–306 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lebtahi, L., Romero, O., Thome, N.: Relations between {K,s + 1}-potent matrices and different classes of complex matrices. Linear Algebra Appl. 438, 1517–1531 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Lebtahi, L., Romero, O., Thome, N.: Algorithms for {K,s + 1}-potent matrix constructions. J. Comput. Appl. Math. 249, 157–162 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lebtahi, L., Romero, O., Thome, N.: Generalized centro-invertible matrices with applications. Appl. Math. Lett. 38, 106–109 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lee, A.: Centrohermitian and skew-centrohermitian matrices. Linear Algebra Appl. 29, 205–210 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Stuart, J., Weaver, J.: Matrices that commute with a permutation. Linear Algebra Appl. 150, 255–265 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Weaver, J.: Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors. Am. Math. Mon. 92, 711–717 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Wikramaratna, R.S.: The centro-invertible matrix: a new type of matrix arising in pseudo-randon number generation. Linear Algebra Appl. 434(1), 144–151 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Wikramaratna, R.S.: The additive congruential random number generator—a special case of a multiple recursive generator. J. Comput. Appl. Math. 216(2), 371–387 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Yasuda, M.: Some properties of commuting and anti-commuting m-involutions. Acta Math. Sci. 32(2), 631–644 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zhongyun, L.: Some properties of centrosymmetric matrices and its applications. Numer. Math. 14, 2 (2005)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultat de MatemàtiquesUniversitat de ValènciaValenciaSpain
  2. 2.Universitat Politècnica de ValènciaValenciaSpain
  3. 3.Instituto Universitario de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain

Personalised recommendations