λ—矩阵的最大公因式与不变因子间的关系及其性质

Relation Between the Greatest Common Factor of the λ—Matrix and Invariant Factor and the Greatest Common Factor's Properties

定义了λ—矩阵的最大公因式,讨论了其性质;证明了λ—矩阵的最大公因式与不变因子间的关系:di(λ)=gcf(Ai()λ).最后指出,利用这一关系可彻底解决λ—矩阵化标准形过程中存在的盲目性问题.

In erties of the this paper,the concepts of the greatest common factor of the X--matrix are defined,the propgreatest common factor are also discussed,and relationship di（λ） = gcf（Ai（λ） ） was proved. Finally,the uncertain problem existed in the process in that λ-matrix convert into normal form was solved.