TY - JOUR
T1 - On the lengths of Jordan chains for eigenvalues on the boundary of numerical range of quadratic operator polynomial
AU - Krupnik, Naum
PY - 2004/7/1
Y1 - 2004/7/1
N2 - We describe a connection between the geometrical structure of the numerical range W(L) of a selfadjoint quadratic operator polynomial L(λ) and the lengths of Jordan chains for eigenvalues on the boundary of the numerical range. Also for each pair of natural numbers m,n (1≤m≤2n) we construct a monic quadratic polynomial Lm,n(λ)=λ2+λC+B with selfadjoint n×n matrices C, B which has an eigenvalue λ0∈∂W(Lm,n) with a Jordan chain of length m.
AB - We describe a connection between the geometrical structure of the numerical range W(L) of a selfadjoint quadratic operator polynomial L(λ) and the lengths of Jordan chains for eigenvalues on the boundary of the numerical range. Also for each pair of natural numbers m,n (1≤m≤2n) we construct a monic quadratic polynomial Lm,n(λ)=λ2+λC+B with selfadjoint n×n matrices C, B which has an eigenvalue λ0∈∂W(Lm,n) with a Jordan chain of length m.
KW - Jordan chains of operator polynomial
KW - Numerical range of operator
KW - Numerical range of operator polynomial
KW - Operator and matrix polynomials
UR - http://www.scopus.com/inward/record.url?scp=2542432379&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2003.07.002
DO - 10.1016/j.laa.2003.07.002
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AN - SCOPUS:2542432379
SN - 0024-3795
VL - 385
SP - 131
EP - 147
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1-3
ER -