On the Numerical Range of Operator Polynomials
F.O. Farid · Linear and Multilinear Algebra · 2002
An upper bound for the number of components of the numerical range of matrix polynomials is established. We also establish a necessary condition and a sufficient condition for the connectedness of the numerical range of a quadratic selfadjoint matrix polynomial. The boundary of the numerical range of linear matrix polynomials is also considered.