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.
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页码：303 / 325
页数：23
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