I have an $n \times n$ lower triangular matrix $A$ where

$$A_{i,j} = {\bf x}_i{\bf x}_j^H,\quad i>j$$

$$A_{ii}=1, \quad 1 \leq i \leq n,$$

and ${\bf x}_i$ is a $1 \times k$ (row) vector, where $k < n$. I need to study $A^{-1}$.

Since matrix $A$ is formed from (roughly) $n k$ elements, but contains (roughly) $n^2$, there could be some special properties. Any input on the structure would be useful. Currently, I use a simple Neumann series to study the behavior of the inverse, but with limited results.