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 $k < m$. I need to study $A^{-1}$.

Since matrix $A$ is formed from (roughly) $m k$ elements, but contains (roughly) $m^2$, 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.

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.

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 $1\times K$ vector, $K<M$.

  I need to study $A^{-1}$. Since the matrix $A$ is formed from (roughly) $MK$ elements, but contains (roughly) $M^2$ there could be some special properties.

  Any input on the structure would be useful. Currently I use a simple Neumann series to study behavior of the inverse, but with limited results.

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 $k < m$. I need to study $A^{-1}$. 

Since matrix $A$ is formed from (roughly) $m k$ elements, but contains (roughly) $m^2$, 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.