On the shape of numerical range of matrix polynomials Original Research Article

The numerical range of an n×n matrix polynomial P(λ)=Amλm+cdots, three dots, centered+A1λ+A0 is defined by image In this paper, we investigate the shape of W(P) by using the notion of local dimension. The numerical range of first order matrix polynomials is always simply connected. The special cases of diagonal matrix polynomials and 2×2 matrix polynomials are also considered.