# Moments of inverses of $(m,n,\beta)$-Laguerre matrices

## TL;DR

This paper establishes conditions under which the moments of inverses of $(m,n,eta)$-Laguerre matrices exist, extending to inverse compound Wishart matrices for specific $eta$ values, thereby enriching the theoretical understanding of these matrix models.

## Contribution

It provides a necessary and sufficient condition for finite moments of inverses of $(m,n,eta)$-Laguerre matrices and extends the results to inverse compound Wishart matrices for $eta=1,2$.

## Key findings

- Necessary and sufficient condition for finite moments of inverses.
- Extension of results to inverse compound Wishart matrices for $eta=1,2$.
- Complements previous theoretical work on matrix moments.

## Abstract

Wishart matrices are one of the fundamental matrix models in multivariate statistics. We consider the classical $(m,n,\beta)$-Laguerre ensemble and give a necessary and sufficient condition for finite moments for the inverse of $(m,n,\beta)$-Laguerre matrices to exist. We extend the result to inverse compound Wishart matrices for the values of $\beta = 1$ and $2$. Our result complements the result by Letac and Massam [6], Matsumoto [7] and Collins et al. [1].