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

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	3349-3359
Number of pages	11
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	43
Issue number	5
DOIs	https://doi.org/10.1007/s40840-019-00873-y
Publication status	Published - 1 Sept 2020

Keywords

Cayley–Hamilton theorem
Doubly infinite matrix
Periodic matrix

ASJC Scopus subject areas

General Mathematics

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10.1007/s40840-019-00873-y

Cite this

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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",

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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

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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

Abstract

Keywords

ASJC Scopus subject areas

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