TY - JOUR
ID - 1056
TI - Properties of matrices with numerical ranges in a sector
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Zhang, D.
AU - Hou, L.
AU - Ma, L.
AD - Department of Mathematics, Shanghai University, Shanghai 200444, China.
Y1 - 2017
PY - 2017
VL - 43
IS - 6
SP - 1699
EP - 1707
KW - Numerical ranges
KW - sector
KW - positive definite
KW - Toeplitz decomposition
DO -
N2 - Let $(A)$ 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 $(S_{alpha})$.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.
UR - http://bims.iranjournals.ir/article_1056.html
L1 - http://bims.iranjournals.ir/article_1056_b52b59d9cddfb9e022bc31ed6322b513.pdf
ER -