An algebraic equation for linear operators

被引：5

作者：

Ng, CT

Zhang, WN ^{[1
]}

机构：

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

[2] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 412卷 / 2-3期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

functional equation; fractional iterate; Babbage's equation; linear operator; canonical decomposition; normal form; matrix equation;

D O I：

10.1016/j.laa.2005.06.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let T be a linear operator on a vector space V, possibly of infinite dimension, over a general field K. We solve the functional equation p(T) = F where p is an element of K[x] and F, an algebraic operator on V, are given. For nilpotent F we give an explicit linear system which determines the solutions by their similarity classes. The method is based on a canonical decomposition theorem. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：303 / 325

页数：23

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