TY - JOUR AU - Yan, Wen PY - 2011/05/25 Y2 - 2024/03/28 TI - Numerical range of a pair of strictly upper triangular matrices JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 30 IS - 1 SE - DO - 10.4067/S0716-09172011000100008 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/77-90 SP - 77-90 AB - <span>Given two strictly upper triangular matrices X, Y ∈ C</span><sub>m×m</sub><span>, we study the range W</span><sub>Y</sub><span> (X) = {trnXn</span><sup>-1</sup><span>Y* : n ∈ N}, where N is the group of unit upper triangular matrices in C</span><sub>m×m</sub><span>. 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</span><sup>k</sup><span>(k = m(m - 1)/2) embedded in N , m = 4.</span> ER -