Journal of Mathematical Sciences

, Volume 141, Issue 6, pp 1586–1600 | Cite as

Joint bounds for the Perron roots of nonnegative matrices with applications

  • Yu. A. Al’pin
  • L. Yu. Kolotilina
  • N. N. Korneeva


Given a finite set {Ax}x ∈ X of nonnegative matrices, we derive joint upper and lower bounds for the row sums of the matrices D−1 A(x) D, x ∈ X, where D is a specially chosen nonsingular diagonal matrix. These bounds, depending only on the sparsity patterns of the matrices A(x) and their row sums, are used to obtain joint two-sided bounds for the Perron roots of given nonnegative matrices, joint upper bounds for the spectral radii of given complex matrices, bounds for the joint and lower spectral radii of a matrix set, and conditions sufficient for all convex combinations of given matrices to be Schur stable. Bibliography: 20 titles.


Spectral Radius Convex Combination Complex Matrice Nonnegative Matrix Sparsity Pattern 
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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • Yu. A. Al’pin
    • 1
  • L. Yu. Kolotilina
    • 2
  • N. N. Korneeva
    • 1
  1. 1.Kazan’ State UniversityKazan’Russia
  2. 2.St.Petersburg Department of the Steklov Mathematical InstituteSt.PetersburgRussia

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