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Abstract
We show that if A = [a_{ij}]^{n}_{i, j=1} is an nbyn complex matrix and A′ = [a′_{i,j}]^{n}_{i, j=1}, where (eqution found), then w(A)≥ w(A′), where w(·) denotes the numerical radius of a matrix. Moreover, if n is odd and a_{12},…,a_{n}_{−1,n,}a_{n1} are all nonzero, then w(A) = w(A′) if and only if A = A′. For an even n, under the same nonzero assumption, we have W(A) =W(A′) if and only if A = A′, where W(·) is the numerical range of a matrix.
Original language  English 

Pages (fromto)  9991014 
Number of pages  16 
Journal  Operators and Matrices 
Volume  11 
Issue number  4 
DOIs  
State  Published  Dec 2017 
Keywords
 Numerical radius
 Numerical range
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Dive into the research topics of 'Lower bounds for the numerical radius'. Together they form a unique fingerprint.Projects
 1 Finished

A Study on ZeroDilation Index of SnMatrix and Companion Matrix
Gau, H.L. (PI)
1/08/16 → 31/07/17
Project: Research