Simplification of symbolic polynomials on non-commutative variables

作     者：de Oliveira, Mauricio C. 

作者机构：Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA 

出 版 物：《LINEAR ALGEBRA AND ITS APPLICATIONS》 (线性代数及其应用)

年 卷 期：2012年第437卷第7期

页      面：1734-1748页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Science Foundation, NSF, (DMS 0757212, DMS 07758) National Science Foundation, NSF Directorate for Mathematical and Physical Sciences, MPS, (0757212) Directorate for Mathematical and Physical Sciences, MPS Ford Motor Company 

主　　题：Linear matrix operators Sylvester operators Noncommutative polynomials Symbolic computation and algorithms 

摘      要：We address the issue of simplifying symbolic polynomials on non-commutative variables. The problem is motivated by applications in optimization and various problems in systems and control. We develop theory for polynomials which are linear in a subset of the variables and develop algorithms to produce representations which have the minimal possible number of terms. The results can handle polynomial matrices as well as block-matrix variables. (C) 2012 Elsevier Inc. All rights reserved.