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


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.


inertia sign pattern matrix tridiagonal matrix 


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  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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