Theq-numerical range of matrix polynomials
Panayiotis Psarrakos, Panayiotis M. Vilamos · Linear and Multilinear Algebra · 2000
Let be a matrix polynomial, where are n×n complex matrices and λ is a complex variable. For a q∊[0,1] the q-numerical range of P(λ)is defined as In this paper we study Wq [Pλ] and our emphasis is on the geometrical properties of Wq [Pλ]. We consider the location of Wq [Pλ]in the complex plane and a theorem concerning the boundary ofWq [Pλ]is also obtained.