The Moore–Penrose inverses of matrices over quaternion polynomial rings

In this paper, we define and discuss the Moore–Penrose inverses of matrices with quaternion polynomial entries. When the Moore–Penrose inverses exist, we prove that Leverrier–Faddeev algorithm works for these matrices by using generalized characteristic polynomials. Furthermore, after studying interpolations for quaternion polynomials, we give an efficient algorithm to compute the Moore–Penrose inverses. We developed a Maple package for quaternion polynomial matrices. All algorithms in this paper are implemented, and tested on examples.