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Czechoslovak Mathematical Journal

, Volume 56, Issue 3, pp 875–883 | Cite as

On the inertia sets of some symmetric sign patterns

  • C. M. da Fonseca
Article

Abstract

A matrix whose entries consist of elements from the set {+, −, 0} is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.

Keywords

inertia sign pattern matrix tridiagonal matrix 

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References

  1. [1]
    B. E. Cain and E. Marques de Sá: The inertia of Hermitian matrices with a prescribed 2 × 2 block decomposition. Linear and Multilinear Algebra 31 (1992), 119–130.MATHMathSciNetGoogle Scholar
  2. [2]
    B. E. Cain and E. Marques de Sá: The inertia of certain skew-triangular block matrices. Linear Algebra Appl. 160 (1992), 75–85.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    C. Eschenbach and C. R. Johnson: A combinatorial converse to the Perron-Frobenius theorem. Linear Algebra Appl. 136 (1990), 173–180.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    C. Eschenbach and C. R. Johnson: Sign patterns that require real, nonreal or pure imaginary eigenvalues. Linear and Multilinear Algebra 29 (1991), 299–311.MATHMathSciNetGoogle Scholar
  5. [5]
    Y. Gao and Y. Shao: The inertia set of nonnegative symmetric sign pattern with zero diagonal. Czechoslovak Math. J. 53 (2003), 925–934.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    F. J. Hall and Z. Li: Inertia sets of symmetric sign pattern matrices. Numer. Math. J. Chinese Univ. (English Ser.) 10 (2001), 226–240.MATHMathSciNetGoogle Scholar
  7. [7]
    F. J. Hall, Z. Li and Di Wang: Symmetric sign pattern matrices that require unique inertia. Linear Algebra Appl. 338 (2001), 153–169.MATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    R. A. Horn and C. R. Johnson: Matrix Analysis, Cambridge University Press, Cambridge. 1985.Google Scholar
  9. [9]
    C. Jeffries and C. R. Johnson: Some sign patterns that preclude matrix stability. SIAM J. Matrix Anal. Appl. 9 (1988), 19–25.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2006

Authors and Affiliations

  • C. M. da Fonseca
    • 1
  1. 1.Departamento de MatemáticaUniversidade de CoimbraCoimbraPortugal

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