Numerical range of a pair of strictly upper triangular matrices


  • Wen Yan Tuskegee University.



Numerical range, Unit upper triangular matrices, Strictly upper triangular matrices.


Given two strictly upper triangular matrices X, Y ? Cm×m, we study the range WY (X) = {trnXn-1Y* : n ? N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of Ck(k = m(m - 1)/2) embedded in N , m = 4.

Author Biography

Wen Yan, Tuskegee University.

Department of Mathematics.


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How to Cite

W. Yan, “Numerical range of a pair of strictly upper triangular matrices”, Proyecciones (Antofagasta, On line), vol. 30, no. 1, pp. 77-90, May 2011.