I'm looking to integrate over the possible entries of an n*n matrix with the following constraints:
$a_{ij} \geq 0 \,\forall\, i,j$
$\sum_{ij} a_{ij}=1$
$\sum_i a_{ki} = \sum_j a_{jk}$
so matrices with non-negative elements which sum to 1, for which the kth column and the kth row have the same sum.
The integral is over $\prod_{ij} da_{ij}$ with these $n$ constraints (since the nth row/column sum is implied by the others).
Is anyone familiar with matrices of this form?
I'm looking to express the integral in a way that will allow me to numerically evaluate it iteratively.