TY - JOUR
T1 - On flat portions on the boundary of the numerical range
AU - Brown, Ethan S.
AU - Spitkovsky, Ilya M.
N1 - Funding Information:
Research of both authors supported in part by NSF Grant DMS-99-88579. ∗ Corresponding author. E-mail addresses: [email protected] (E.S. Brown), [email protected] (I.M. Spitkovsky). URL: http://www.math.wm.edu/∼ilya (I.M. Spitkovsky).
PY - 2004/10/1
Y1 - 2004/10/1
N2 - The paper is devoted to matrices with flat portions on the boundary of their numerical range. A constructive criterion for such portions to exist is obtained in case of tridiagonal matrices, and a particular case of continuant matrices is considered. As an application, the cases of (arbitrary) 3×3 and 4×4 matrices are treated. It is shown, in particular, that the sharp bound for the number of flat portions on the boundary of the numerical range for 4×4 matrices is four (three, if the matrices are assumed unitarily irreducible).
AB - The paper is devoted to matrices with flat portions on the boundary of their numerical range. A constructive criterion for such portions to exist is obtained in case of tridiagonal matrices, and a particular case of continuant matrices is considered. As an application, the cases of (arbitrary) 3×3 and 4×4 matrices are treated. It is shown, in particular, that the sharp bound for the number of flat portions on the boundary of the numerical range for 4×4 matrices is four (three, if the matrices are assumed unitarily irreducible).
KW - Numerical range
KW - Tridiagonal matrices
KW - Unitary (ir)reducibility
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U2 - 10.1016/j.laa.2004.04.009
DO - 10.1016/j.laa.2004.04.009
M3 - Article
AN - SCOPUS:4344687566
SN - 0024-3795
VL - 390
SP - 75
EP - 109
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1-3
ER -