Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43620171130Properties of matrices with numerical ranges in a sector169917071056END.ZhangDepartment of Mathematics, Shanghai University, Shanghai 200444, China.L.HouDepartment of Mathematics, Shanghai University, Shanghai 200444, China.L.MaDepartment of Mathematics, Shanghai University, Shanghai 200444, China.Journal Article20160513Let $(A)$ be a complex $(ntimes n)$ matrix and assume that the numerical range of $(A)$ lies in the set of a sector of half angle $(alpha)$ denoted by $(S_{alpha})$. We prove the numerical ranges of the conjugate, inverse and Schur complement of any order of $(A)$ are in the same $(S_{alpha})$.<br />The eigenvalues of some kinds of matrix product and numerical ranges of hadmard product, star-congruent matrix and unitary matrix of polar decompostion are also included in the same sector. Furthermore, we extend some inequalities about eigenvalues and singular values and the linear fractional maps to this class of matrices.http://bims.iranjournals.ir/article_1056_b52b59d9cddfb9e022bc31ed6322b513.pdf