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On the Hu-Hurley-Tam conjecture concerning the generalized numerical range by Che-Man Cheng; Chi-Kwong Li is a Mathematics article available to read on EtoBox.
What is On the Hu-Hurley-Tam conjecture concerning the generalized numerical range about?
Suppose m and n are integers such that 1 m n, and H is a subgroup of the symmetric group S m of degree m. Define the generalized matrix function associated with the principal character of the group H on an m × m matrix B = (b ij ) by b jσ (j) , and define the generalized numerical range of an n × n matrix A associated with d H by Hu, Hurley and Tam made the following conjecture: Suppose H = S m , 2 m n with (m, n) / = (2, 2). Let A ∈ M n be a normal matrix. Then W H (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 < n. Some techniques are developed to show that the conjecture is valid under more restrictive assumptions.
Who reads On the Hu-Hurley-Tam conjecture concerning the generalized numerical range?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Che-Man Cheng; Chi-Kwong Li
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0024-3795)
- Published
- 2000
- Language
- EN
- Field
- Mathematics (Physical Sciences)