On Hyper–Regularity and Unimodularity of Ore Polynomial Matrices

Abstract

We investigate Ore polynomial matrices, i. e., matrices with polynomial entries in d/dt whose coefficients are meromorphic functions in t and as such constitute a non-commutative ring. In particular, we study the properties of hyper-regularity and unimodularity of such matrices and derive conditions which make it possible to efficiently check for these characteristics. In addition, this approach enables computation of hyper-regular left and right and unimodular inverses.

Keywords

• ore polynomial matrices
• hyper-regularity
• unimodularity
• meromorphic functions
• differential operator
• noncommutativity
• algorithm
• hyper-regular inverse