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Circularity of the numerical range. (English) Zbl 0809.15012

The authors give an equivalent condition on a 3 or 4-square real upper triangular matrix for its numerical range to be a circular disk centered at the origin. Some sufficient condition on certain sparse matrices for the same problem are also obtained.

MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
Full Text: DOI

References:

[1] Bassett, L.; Maybee, J.; Quirk, J., Qualitative economics and the scope of the correspondence principle, Econometrica, 36, 544-563 (1968) · Zbl 0217.26802
[2] Brualdi, R.; Ryser, H. J., Combinatorial Matrix Theory (1991), Cambridge U.P · Zbl 0746.05002
[3] Davidson, K. R.; Holbrook, J. A.R., Numerical radii of zero-one matrices, Michigan Math. J., 35, 261-267 (1988) · Zbl 0692.47005
[4] Li, C. K.; Tsing, N. K., Matrices with circular symmetry on their unitary orbits and C-numerical ranges, Proc. Amer. Math. Soc., 111, 19-28 (1991) · Zbl 0719.15017
[5] Marcus, M.; Pesce, C., Computer generated numerical ranges and some resulting theorems, Linear and Multilinear Algebra, 20, 121-157 (1987) · Zbl 0626.65038
[6] Marcus, M.; Shure, B. N., The numerical range of certain 0, 1-matrices, Linear and Multilinear Algebra, 7, 111-120 (1979) · Zbl 0395.15010
[7] Swamy, M. N.S.; Thulasiraman, K., Graphs, Networks, and Algorithms (1981), Wiley: Wiley New York · Zbl 0528.94034
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