The higher rank numerical range of matrix polynomials

Abstract

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.

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

References in corpus (1)

• Quantum error correction and generalized numerical ranges

Cited by in corpus (1)

• The higher rank numerical range of nonnegative matrices