TY - JOUR
T1 - Lower bounds for the numerical radius
AU - Gau, Hwa Long
AU - Wu, Pei Yuan
N1 - Publisher Copyright:
© 2017, Element D.O.O. All rights reserved.
PY - 2017/12
Y1 - 2017/12
N2 - We show that if A = [aij]ni, j=1 is an n-by-n complex matrix and A′ = [a′i,j]ni, 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 a12,…,an−1,n,an1 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.
AB - We show that if A = [aij]ni, j=1 is an n-by-n complex matrix and A′ = [a′i,j]ni, 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 a12,…,an−1,n,an1 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.
KW - Numerical radius
KW - Numerical range
UR - http://www.scopus.com/inward/record.url?scp=85034978342&partnerID=8YFLogxK
U2 - 10.7153/oam-2017-11-69
DO - 10.7153/oam-2017-11-69
M3 - 期刊論文
AN - SCOPUS:85034978342
SN - 1846-3886
VL - 11
SP - 999
EP - 1014
JO - Operators and Matrices
JF - Operators and Matrices
IS - 4
ER -