TY - JOUR
T1 - On eigenvalues and boundary curvature of the numerical range
AU - Caston, Lauren
AU - Savova, Milena
AU - Spitkovsky, Ilya
AU - Zobin, Nahum
N1 - Funding Information:
ø This research was conducted while the first two authors were participating at the College of William and Mary’s Research Experience for Undergraduates program in the summer of 1999 and was supported by NSF grant DMS-96-19577. M. Savova received support from Mount Holyoke College, and I. Spitkovsky was also supported by NSF grant DMS-98-00704. ∗ Corresponding author. E-mail addresses: [email protected] (L. Caston), [email protected] (M. Savova), [email protected] (I. Spitkovsky), [email protected] (N. Zobin).
PY - 2001/1/1
Y1 - 2001/1/1
N2 - Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.
AB - Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.
KW - Curvature
KW - Eigenvalues
KW - Numerical range
KW - Primary 47A12
KW - Secondary 15A42, 14H50
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U2 - 10.1016/S0024-3795(00)00231-7
DO - 10.1016/S0024-3795(00)00231-7
M3 - Article
AN - SCOPUS:0035578974
SN - 0024-3795
VL - 322
SP - 129
EP - 140
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1-3
ER -