Residential College | false |
Status | 已發表Published |
On the Hu-Hurley-Tam conjecture concerning the generalized numerical range | |
Cheng C.-M.1; Li C.-K.2 | |
2000-01 | |
Source Publication | Linear Algebra and Its Applications |
ISSN | 0024-3795 |
Volume | 305Issue:1-3Pages:87-97 |
Abstract | Suppose m and n are integers such that 1≤m≤n, and H is a subgroup of the symmetric group S of degree m. Define the generalized matrix function associated with the principal character of the group H on an m×m matrix B=(b) byd(B)=∑∏ b,and define the generalized numerical range of an n×n matrix A associated with d byW(A)=(d (V*AV):Visn×msuchthatV*V=I).It is known that W(A) is convex if m=1 or if m=n=2. Hu, Hurley and Tam made the following conjecture: Suppose H=S, 2≤m≤n with (m,n)≠(2,2). Let A∈M be a normal matrix. Then W(A) is convex if and only if A is a multiple of a Hermitian matrix. In this note, counter examples are given to show that the conjecture is not true when m |
Keyword | 15a60 Decomposable Numerical Range Principal Character |
DOI | https://doi.org/10.1016/S0024-3795(99)00228-1 |
URL | View the original |
Indexed By | SCIE |
Language | 英語English |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000084823700007 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Affiliation | 1.Faculty of Science and Technology, University of Macau, Macau 2.Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, USA |
First Author Affilication | Faculty of Science and Technology |
Recommended Citation GB/T 7714 | Cheng C.-M.,Li C.-K.. On the Hu-Hurley-Tam conjecture concerning the generalized numerical range[J]. Linear Algebra and Its Applications,2000,305(1-3):87-97. |
APA | Cheng C.-M.,&Li C.-K..(2000).On the Hu-Hurley-Tam conjecture concerning the generalized numerical range.Linear Algebra and Its Applications,305(1-3),87-97. |
MLA | Cheng C.-M.,et al."On the Hu-Hurley-Tam conjecture concerning the generalized numerical range".Linear Algebra and Its Applications 305.1-3(2000):87-97. |
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