Is it possible to express the product: $ \frac{\prod_{i < j} (a_i - a_j)(b_i - b_j) }{\prod_{i,j} (a_i - b_j) }$ as the determinant of a single matrix ?
This comes from a physics paper. Should be similar to a Vandermonde determinant.
EDIT: Obviously, I do not want a $1 \times 1$ matrix whose single entry as the answer. Why are Hilbert matrices or Toeplitz matrices or Cauchy matrices, the natural choices then ? Sorry.