Representation of doubly infinite matrices as non-commutative Laurent series

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 matrice...
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Autor*in:	Arenas-Herrera María Ivonne [verfasserIn] Verde-Star Luis [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	doubly infinite matrices non-commutative laurent series infinite hessenberg matrices similarity of infinite matrices pincherle derivatives.

Übergeordnetes Werk:	In: Special Matrices - De Gruyter, 2015, 5(2017), 1, Seite 250-257
Übergeordnetes Werk:	volume:5 ; year:2017 ; number:1 ; pages:250-257

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1515/spma-2017-0018

Katalog-ID:	DOAJ061050040

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allfieldsSound	10.1515/spma-2017-0018 doi (DE-627)DOAJ061050040 (DE-599)DOAJ9adc207863c04372aab1158e6fc0916c DE-627 ger DE-627 rakwb eng QA1-939 Arenas-Herrera María Ivonne verfasserin aut Representation of doubly infinite matrices as non-commutative Laurent series 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. doubly infinite matrices non-commutative laurent series infinite hessenberg matrices similarity of infinite matrices pincherle derivatives. Mathematics Verde-Star Luis verfasserin aut In Special Matrices De Gruyter, 2015 5(2017), 1, Seite 250-257 (DE-627)777285444 (DE-600)2753755-9 23007451 nnns volume:5 year:2017 number:1 pages:250-257 https://doi.org/10.1515/spma-2017-0018 kostenfrei https://doaj.org/article/9adc207863c04372aab1158e6fc0916c kostenfrei https://doi.org/10.1515/spma-2017-0018 kostenfrei https://doaj.org/toc/2300-7451 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 5 2017 1 250-257
language	English
source	In Special Matrices 5(2017), 1, Seite 250-257 volume:5 year:2017 number:1 pages:250-257
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topic_facet	doubly infinite matrices non-commutative laurent series infinite hessenberg matrices similarity of infinite matrices pincherle derivatives. Mathematics
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callnumber-first	Q - Science
author	Arenas-Herrera María Ivonne
spellingShingle	Arenas-Herrera María Ivonne misc QA1-939 misc doubly infinite matrices misc non-commutative laurent series misc infinite hessenberg matrices misc similarity of infinite matrices misc pincherle derivatives. misc Mathematics Representation of doubly infinite matrices as non-commutative Laurent series
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topic_title	QA1-939 Representation of doubly infinite matrices as non-commutative Laurent series doubly infinite matrices non-commutative laurent series infinite hessenberg matrices similarity of infinite matrices pincherle derivatives
topic	misc QA1-939 misc doubly infinite matrices misc non-commutative laurent series misc infinite hessenberg matrices misc similarity of infinite matrices misc pincherle derivatives. misc Mathematics
topic_unstemmed	misc QA1-939 misc doubly infinite matrices misc non-commutative laurent series misc infinite hessenberg matrices misc similarity of infinite matrices misc pincherle derivatives. misc Mathematics
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title	Representation of doubly infinite matrices as non-commutative Laurent series
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title_full	Representation of doubly infinite matrices as non-commutative Laurent series
author_sort	Arenas-Herrera María Ivonne
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title_sort	representation of doubly infinite matrices as non-commutative laurent series
callnumber	QA1-939
title_auth	Representation of doubly infinite matrices as non-commutative Laurent series
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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	Representation of doubly infinite matrices as non-commutative Laurent series
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