Resumen

YAN, Wen. Numerical range of a pair of strictly upper triangular matrices. Proyecciones (Antofagasta) [online]. 2011, vol.30, n.1, pp. 77-90. ISSN 0716-0917.  doi: 10.4067/S0716-09172011000100008.

Given two strictly upper triangular matrices X, Y ? C_m×m, we study the range W_Y (X) = {trnXn^-1Y* : n ? N}, where N is the group of unit upper triangular matrices in C_m×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 C^k (k = m(m - 1)/2) embedded in N , m = 4.

Palabras clave : Numerical range; unit upper triangular matrices; strictly upper triangular matrices.