Consider the upper traingular $N \times N$ matrix
$$\left(\begin{array}{cccccccc} 0 & b_{1} & \dots & b_{q} & 0 & 0 & \dots & 0\\ \vdots & 0 & b_{1} & \dots & b_{q} & 0 & \dots & 0\\ \vdots & & \ddots & & & & & \vdots\\ \vdots & & & 0 & b_{1} & \dots & b_{q} & 0\\ \vdots & & & & 0 & b_{1} & \dots & b_{q}\\ \vdots & & & & & 0 & \dots & 0\\ \vdots & & & & & & \ddots & \vdots\\ 0 & \dots & \dots & \dots & \dots & \dots & \dots & 0 \end{array}\right)$$
Is there a name for matrices of this form?