Theory and recursive computation of 1-D matrix Pade approximants

Given a matrix power series, it is shown that (except possibly in certain derogatory cases) a recurrence relation relates the
[L+ l/M+1}
[L/M], [L- l/M- 1]
order Pade approximants, the existence of each of which is guaranteed from validity of a certain rank condition on the corresponding set of characterizing matrices possessing a block-Hankel structure.