Inversion of isoclinal matrices

Abstract:

Triangular matrices (over the reals), whose elements satisfy ${a_{i,j}} = {a_{i + 1,j + 1}}$, can be mapped algebraically into the rational functions to facilitate determination of inverses and factors of the matrices. It is further shown in this note that these methods can be extended to the nontriangular forms to obtain inverses or demonstrate singular cases. Applications are made to certain matrices of Hessenberg type.