A remark on the generalized numerical range of a normal matrix
Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 179-180
Voir la notice de l'article provenant de la source Cambridge University Press
Let A be an n × n complex normal matrix and let (A) = {diag UAU*: U is unitary) where U* is the conjugate transpose of U. It is known that (A) may not be convex [1, 3] and it is convex when A is Hermitian [1, 2]. In this note we show that (A) is convex if and only if the eigenvalues of A are collinear (i.e. there exist complex numbers α ( ≠ 0) and β such that αA + βi is Hermitian).
Au-Yeung, Yik-Hoi; Sing, Fuk-Yum. A remark on the generalized numerical range of a normal matrix. Glasgow mathematical journal, Tome 18 (1977) no. 2, pp. 179-180. doi: 10.1017/S0017089500003244
@article{10_1017_S0017089500003244,
author = {Au-Yeung, Yik-Hoi and Sing, Fuk-Yum},
title = {A remark on the generalized numerical range of a normal matrix},
journal = {Glasgow mathematical journal},
pages = {179--180},
year = {1977},
volume = {18},
number = {2},
doi = {10.1017/S0017089500003244},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500003244/}
}
TY - JOUR AU - Au-Yeung, Yik-Hoi AU - Sing, Fuk-Yum TI - A remark on the generalized numerical range of a normal matrix JO - Glasgow mathematical journal PY - 1977 SP - 179 EP - 180 VL - 18 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500003244/ DO - 10.1017/S0017089500003244 ID - 10_1017_S0017089500003244 ER -
%0 Journal Article %A Au-Yeung, Yik-Hoi %A Sing, Fuk-Yum %T A remark on the generalized numerical range of a normal matrix %J Glasgow mathematical journal %D 1977 %P 179-180 %V 18 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500003244/ %R 10.1017/S0017089500003244 %F 10_1017_S0017089500003244
Fillmore, P. A. and Williams, J. P., Some convexity theorems for matrices, Glasgow Math. J. 12 (1971), 110–116. Google Scholar | DOI
Horn, A, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620–630. Google Scholar | DOI
Lerer, L. E., On the diagonal elements of normal matrices (Russian), Mat. Issled. 2 (1967). 156–163. Google Scholar
Cité par Sources :