Abstract: In this paper, we study the J-C-numerical range of a set or a tuple of matrices and investigate their basic properties. In this paper, we study the J-C-numerical range of a set or a tuple of matrices and investigate their basic properties. Also, we give the conditions of star-shapedness of the J-C-numerical range. Finally, we generalize these results to a set of matrices. تفاصيل المقالة