Abstract
Some procedures are proposed for well known as well as new factorizations of the inverses of nonsingular generalized Hessenberg matrices . Moreover, we take advantage in such decompositions of low-rank structures of Hessenberg-like matrices . This suite of decompositions includes various cases when the matrix is nonsingular and also the case when has a unique factorization. Finally as a main result, a simple and constructive characterization of the nonsingular generalized Hessenberg matrices and their inverses are presented.
Acknowledgements
The authors thank to the reviewers by their valuable help in the improvement of this article.