Some Counterexamples for Cayley–Hamilton Theorem for Doubly Infinite Matrices

被引：0
|
作者：
Roksana Słowik
机构：
[1] Silesian University of Technology,Faculty of Applied Mathematics
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2020年 / 43卷
关键词：
Cayley–Hamilton theorem; Doubly infinite matrix; Periodic matrix; Primary 15A99; 15B99; 47B99;
D O I：
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学科分类号：
摘要：
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.
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页码：3349 / 3359
页数：10
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