# what is the name of this matrix? does it have any special characteristics?

does anyone know the name of this matrix or if it has any special characteristics or how to calculate its inverse efficiently e.g. in a closed-form?

[ \begin{array}{llllll} a_{11} & a_{12}& a_{13} & a_{14} & \dots & a_{1L} \\ q_1 & a_{22} & a_{23} & a_{23} & \dots & a_{2L} \\ q_2 & q_1 & a_{33} & a_{34} & \dots & a_{3L} \\ q_3 & q_2 & q_1 & a_{44} & \dots & a_{3L} \\ q_4 & q_3 & q_2 & q_1 & \dots & a_{3L} \\ \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\ q_L & q_{L-1} & q_{L-2} & q_{L-3} & \dots & a_{LL}\\ \end{array}]

hint: the lower triangle consists of diagonals with the same value.

This matrix is not always invertible, e.g. if $a_{i,j} = 0$ for every $i,j$ or if $a_{i,j}=q_i=c$ for every $i,j$.