# Representation of doubly infinite matrices as non-commutative Laurent series

María Ivonne Arenas-Herrera; Luis Verde-Star

Special Matrices (2017)

- Volume: 5, Issue: 1, page 250-257
- ISSN: 2300-7451

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topMaría Ivonne Arenas-Herrera, and Luis Verde-Star. "Representation of doubly infinite matrices as non-commutative Laurent series." Special Matrices 5.1 (2017): 250-257. <http://eudml.org/doc/288504>.

@article{MaríaIvonneArenas2017,

abstract = {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.},

author = {María Ivonne Arenas-Herrera, Luis Verde-Star},

journal = {Special Matrices},

keywords = {Doubly infinite matrices; non-commutative Laurent series; infinite Hessenberg matrices; similarity of infinite matrices; Pincherle derivatives.},

language = {eng},

number = {1},

pages = {250-257},

title = {Representation of doubly infinite matrices as non-commutative Laurent series},

url = {http://eudml.org/doc/288504},

volume = {5},

year = {2017},

}

TY - JOUR

AU - María Ivonne Arenas-Herrera

AU - Luis Verde-Star

TI - Representation of doubly infinite matrices as non-commutative Laurent series

JO - Special Matrices

PY - 2017

VL - 5

IS - 1

SP - 250

EP - 257

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/288504

ER -

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