摘要
给出域上上三角矩阵的等价标准型.作为应用,证明了一个秩r上三角矩阵可分解为有限个秩s上三角矩阵的和,并证明了域上上三角矩阵环的每个理想都是主理想,且由唯一的约化标准上三角矩阵生成.
We gave the equivalent canonical form of a upper triangular matrix over a field. As applications,we proved that a upper triangular rank-r matrix could be decomposed into a sum of finitely many upper triangular rank-s matrices; we also proved that each ideal of the ring of all upper triangular matrices over a field was a principal ideal,which was generated by a unique reduced canonical upper triangular matrix.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2016年第2期157-160,共4页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:J1310022
11371165)
关键词
上三角矩阵
等价标准型
秩
理想
upper triangular matrix
equivalent canonical form
rank
ideal
