Further results on generalized centro-invertible matrices

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 


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  1. 1.
    Abu-Jeib, I.: Centrosymmetric matrices: properties and an alternative approach. Can. Appl. Math. Q. 10(4), 429–445 (2002)MathSciNetMATHGoogle 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)MathSciNetCrossRefMATHGoogle 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)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    El-Mikkawy, M., Atlan, F.: On solving centrosymmetric linear systems. Appl. Math. 4, 21–32 (2013)CrossRefMATHGoogle 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).  https://doi.org/10.1051/epjconf/201610801004 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)MathSciNetCrossRefMATHGoogle 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)MathSciNetCrossRefMATHGoogle 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)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Lebtahi, L., Romero, O., Thome, N.: Generalized centro-invertible matrices with applications. Appl. Math. Lett. 38, 106–109 (2014)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Lee, A.: Centrohermitian and skew-centrohermitian matrices. Linear Algebra Appl. 29, 205–210 (1980)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Stuart, J., Weaver, J.: Matrices that commute with a permutation. Linear Algebra Appl. 150, 255–265 (1991)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Weaver, J.: Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors. Am. Math. Mon. 92, 711–717 (1985)MathSciNetCrossRefMATHGoogle 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)MathSciNetCrossRefMATHGoogle 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)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Yasuda, M.: Some properties of commuting and anti-commuting m-involutions. Acta Math. Sci. 32(2), 631–644 (2012)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Zhongyun, L.: Some properties of centrosymmetric matrices and its applications. Numer. Math. 14, 2 (2005)MathSciNetMATHGoogle Scholar

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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

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