Some Counterexamples for Cayley–Hamilton Theorem for Doubly Infinite Matrices

Roksana Słowik

doi:10.1007/s40840-019-00873-y

Some Counterexamples for Cayley–Hamilton Theorem for Doubly Infinite Matrices

Roksana Słowik

Katedra Matematyki (RMS/RMS1)

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

Abstrakt

We study the question about generalization of the Cayley–Hamilton theorem. Namely, the problem if for every banded periodic doubly infinite matrix A there exists polynomial Q such that Q(A) is a matrix with constant diagonals. We present a class of doubly infinite matrices for which such polynomial does not exist.

Język oryginału	angielski
Strony (od–do)	3349-3359
Liczba stron	11
Czasopismo	Bulletin of the Malaysian Mathematical Sciences Society
Tom	43
Numer wydania	5
Identyfikatory DOI	https://doi.org/10.1007/s40840-019-00873-y
Status publikacji	Opublikowano - 1 wrz 2020

Obszary tematyczne ASJC Scopus

Matematyka ogólna

Uzyskaj dostęp do dokumentu

10.1007/s40840-019-00873-y

Inne pliki i linki

Link do publikacji w Scopus

Cytowanie

@article{b1844293e66a4034b9e4d99d37a92dfe,

title = "Some Counterexamples for Cayley{\textendash}Hamilton Theorem for Doubly Infinite Matrices",

abstract = "We study the question about generalization of the Cayley{\textendash}Hamilton theorem. Namely, the problem if for every banded periodic doubly infinite matrix A there exists polynomial Q such that Q(A) is a matrix with constant diagonals. We present a class of doubly infinite matrices for which such polynomial does not exist.",

keywords = "Cayley{\textendash}Hamilton theorem, Doubly infinite matrix, Periodic matrix",

author = "Roksana S{\l}owik",

note = "Publisher Copyright: {\textcopyright} 2019, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.",

year = "2020",

month = sep,

day = "1",

doi = "10.1007/s40840-019-00873-y",

language = "English",

volume = "43",

pages = "3349--3359",

journal = "Bulletin of the Malaysian Mathematical Sciences Society",

issn = "0126-6705",

publisher = "Springer Singapore",

number = "5",

}

TY - JOUR

T1 - Some Counterexamples for Cayley–Hamilton Theorem for Doubly Infinite Matrices

AU - Słowik, Roksana

PY - 2020/9/1

Y1 - 2020/9/1

N2 - We study the question about generalization of the Cayley–Hamilton theorem. Namely, the problem if for every banded periodic doubly infinite matrix A there exists polynomial Q such that Q(A) is a matrix with constant diagonals. We present a class of doubly infinite matrices for which such polynomial does not exist.

AB - We study the question about generalization of the Cayley–Hamilton theorem. Namely, the problem if for every banded periodic doubly infinite matrix A there exists polynomial Q such that Q(A) is a matrix with constant diagonals. We present a class of doubly infinite matrices for which such polynomial does not exist.

KW - Cayley–Hamilton theorem

KW - Doubly infinite matrix

KW - Periodic matrix

UR - https://www.scopus.com/pages/publications/85076287307

U2 - 10.1007/s40840-019-00873-y

DO - 10.1007/s40840-019-00873-y

M3 - Article

AN - SCOPUS:85076287307

SN - 0126-6705

VL - 43

SP - 3349

EP - 3359

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 5

ER -

Some Counterexamples for Cayley–Hamilton Theorem for Doubly Infinite Matrices

Abstrakt

Obszary tematyczne ASJC Scopus

Uzyskaj dostęp do dokumentu

Inne pliki i linki

Fingerprint

Cytowanie