Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

Hwa-Long Gau, Ming-Cheng Tsai, Han-Chun Wang

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form $$[{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}],$$ where the $a_j$'s, call…