The boundary of higher rank numerical ranges

The rank-k  -numerical range of an n×nn×n matrix A is defined asΛk(A)={λ∈C:PAP=λPfor some rankkorthogonal projectionP}.This study presents a method to generate the boundary of Λk(A)Λk(A), and examines the flat portions of the boundary of the rank-k-numerical range of a matrix associated with a roulette curve. A sufficient condition is given to ensure that the rank-k-numerical range is not attainable by a classical numerical range.