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On the Hu-Hurley-Tam conjecture concerning the generalized numerical range
Cheng,Che Man1; Li,Chi Kwong2
Source PublicationLinear Algebra and Its Applications
AbstractSuppose 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, counterexamples are given to show that the conjecture is not true when m
Keyword15A60 Decomposable numerical range Principal character
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Scopus ID2-s2.0-0034400896
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Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Faculty of Science and Technology,University of Macau,Macau,China
2.Department of Mathematics,Coll. William Mary,P.O. Box 8795,Williamsburg, VA 23187-8795,United States
First Author AffilicationFaculty of Science and Technology
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GB/T 7714
Cheng,Che Man,Li,Chi Kwong. 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,Che Man,&Li,Chi Kwong.(2000).On the Hu-Hurley-Tam conjecture concerning the generalized numerical range.Linear Algebra and Its Applications,305(1-3),87-97.
MLA Cheng,Che Man,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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