On the Block Numerical Range of Nonnegative Matrices
K.-H. Förster, Niels Hartanto · Birkhäuser Basel eBooks · 2008
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.