On higher rank numerical hulls of normal matrices

‎In this paper‎, ‎some algebraic and geometrical properties of the rank-k numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank-۱ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form A_۱ \oplus i A_۲‎, ‎where A_۱ and A_۲ are Hermitian‎, ‎are investigated‎. ‎The higher rank numerical hulls of the basic circulant matrix‎ ‎are also studied‎.