The higher rank numerical range of matrix polynomials

Details The higher rank numerical range of matrix polynomials The higher rank numerical range of matrix polynomials

2011-04-07

arxiv.org/abs/1104.1341v1

Mathematics

Rings and Algebras

18 pages, 4 figures, 10th "Workshop on Numerical Ranges and Numerical Radii" (WONRA), Krakow, Poland 2010

Scientific paper

The notion of the higher rank numerical range $\Lambda_{k}(L(\lambda))$ for matrix polynomials $L(\lambda)=A_{m}\lambda^{m}+...+A_{1}\lambda+A_{0}$ is introduced here and some fundamental geometrical properties are investigated. Further, the sharp points of $\Lambda_{k}(L(\lambda))$ are defined and their relation to the numerical range $w(L(\lambda))$ is presented. A connection of $\Lambda_{k}(L(\lambda))$ with the vector-valued higher rank numerical range $\Lambda_{k}(A_{0},..., A_{m})$ is also discussed.

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