Representation of doubly infinite matrices as non-commutative Laurent series

• Autorzy: María Ivonne Arenas-Herrera , Luis Verde-Star
• Języki publikacji: EN

Abstrakty

EN

We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices. We show that such representation is a simple and useful tool for computation purposes and also to obtain general properties of the matrices related with inversion, similarity, commutativity, and Pincherle derivatives. The diagonal representation allows us to consider the ring of doubly infinite lower Hessenberg matrices over a ring R as a ring of Laurent series in one indeterminate, with coefficients in the ring of R-valued sequences that don’t commute with the indeterminate.

Słowa kluczowe

EN

Doubly infinite matrices; non-commutative Laurent series; infinite Hessenberg matrices; similarity of infinite matrices; Pincherle derivatives.

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 250-257

Daty

wydano

2017-11-27

otrzymano

2017-10-11

zaakceptowano

2017-10-27

online

2017-11-16

Twórcy

autor

María Ivonne Arenas-Herrera

• ,

autor

Luis Verde-Star

• ,

Identyfikatory

DOI

10.1515/spma-2017-0018