Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416031 | Linear Algebra and its Applications | 2016 | 17 Pages |
Abstract
It is known that the numerical radius of the Hadamard product AâB of two n-by-n matrices A and B is related to those of A and B by (a) w(AâB)â¤2w(A)w(B), (b) w(AâB)â¤w(A)w(B) if one of A and B is normal, and (c) w(AâB)â¤(maxiâ¡aii)w(B) if A=[aij]i,j=1n is positive semidefinite. In this paper, we give complete characterizations of A and B for which the equality is attained. The matrices involved can be considered as elaborate generalizations of the equality-attaining A=[00a0] and B=[00b0] for (a), A=[a100a2] (|a1|â¥|a2|) and B=[w(B)âââ] for (b), and A=[a1a3a2a4]â¥0 (a1â¥a4) and B=[w(B)âââ] for (c).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hwa-Long Gau, Pei Yuan Wu,