Some Counterexamples for Cayley-Hamilton Theorem for Doubly Infinite Matrices

被引：0

作者：

Slowik, Roksana ^{[1
]}

机构：

[1] Silesian Tech Univ, Fac Appl Math, Kaszubska 23, PL-44100 Gliwice, Poland

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 05期

关键词：

Cayley-Hamilton theorem; Doubly infinite matrix; Periodic matrix;

D O I：

10.1007/s40840-019-00873-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页码：3349 / 3359

页数：11

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