A tabular methodology to identify minimal row degrees for Matrix Padé Approximants

In this paper we propose a tabular procedure for identifying sets of minimal row degrees corresponding to Matrix Padé Approximants. The objective is to make it easier to interpret and properly apply them in various fields. When considering formal matrix power series with k×mk×m coefficients, it is useful to examine the linearly dependent rows that are in the last kk rows in certain Hankel matrices corresponding to the coefficients of the series. A list of properties and suitable examples are added not only by way of illustration but also because they are an original part of the method, having been chosen to teach the procedure and to underscore certain precautions to be taken.