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On the Hu-Hurley-Tam conjecture concerning the generalized numerical range
Cheng C.-M.1; Li C.-K.2
Source PublicationLinear Algebra and Its Applications

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

Keyword15a60 Decomposable Numerical Range Principal Character
URLView the original
Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000084823700007
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Affiliation1.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 AffilicationFaculty 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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