On the Block Numerical Range of Nonnegative Matrices

  • K.-H. Förster
  • N. Hartanto
Part of the Operator Theory: Advances and Applications book series (OT, volume 188)


We present a Perron-Frobenius Theory for the block numerical range of entrywise nonnegative square matrices similar to that known for the special cases of the spectrum and of the standard numerical range. For irreducible matrices we prove a corresponding version of Wielandt’s Lemma. With help of the Frobenius Form we study the block numerical range of a nonnegative matrix and its peripheral part. Finally we give an application to the numerical range of Perron Polynomials.


Matrix Polynomial Nonnegative Matrix Numerical Range Nonnegative Matrice Irreducible Matrix 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • K.-H. Förster
    • 1
  • N. Hartanto
    • 1
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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