Abstract Using the para-equivalent transform, we propose a method for calculating
the J-spectrum factorization for the full rank para-Hermite polynomial matrix. For a
full rank para-Hermite polynomial matrix, we transform it into a uni-module full rank
para-Hermite polynomial matrix by para-equivalent transform at first, then into a full
rank constant symmetric matrix, and into a J_ matrix at last. Accumulating these
transforms, we obtain the J spectrum factorization. Based on the programming package
for polynomial matrix developed by the authors, an algorithm which realizes the
proposed method is given. The numerical example indicates this method is useful.