Numerical range of linear pencils

AbstractConsider a linear pencil Aλ+B, where A and B are n×n complex matrices. The numerical range of Aλ+B is defined asW(Aλ+B)=λ∈C:x*(Aλ+B)x=0forsomenonzerox∈Cn.In this paper, we study the geometrical properties of W(Aλ+B), with emphasis to its boundary. An answer to the problem of the numerical approximation of W(Aλ+B), when one of the coefficients A and B is Hermitian, is presented. The numerical range of a matrix on an indefinite inner product space is also considered