Line segments on the boundary of the numerical ranges of some tridiagonal matrices

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Ilya M. Spitkovsky
Claire Marie Thomas


Tridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described.

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