Abstract
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.
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© 2008 Birkhäuser Verlag Basel/Switzerland
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Förster, KH., Hartanto, N. (2008). On the Block Numerical Range of Nonnegative Matrices. In: Behrndt, J., Förster, KH., Langer, H., Trunk, C. (eds) Spectral Theory in Inner Product Spaces and Applications. Operator Theory: Advances and Applications, vol 188. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8911-6_6
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DOI: https://doi.org/10.1007/978-3-7643-8911-6_6
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