以矩阵左半张量积为工具,研究了几种不同类型矩阵方程的半张量积表示,最后给出了它在Hautus方程中的应用.

以矩阵左半张量积为工具,研究了几种不同类型的线性映射的矩阵展开表示.作为特殊情况,给出了Lya-punov映射、辛映射、伴随映射、共轭映射的相关表示.最后给出了这种矩阵形式在李代数中的应用.

By using correlative equalities and inequalities about ranks of matrices that two matrices act common product,and equalities about the rank of kronecker product,the ranks that two matrices act left semi-tensor product are given.Then,interrelated equalities and inequalities about the rank of matrices are researched.

This paper considers the problem of constructing two bordered diagonal matrices from their eigenpairs. The two bordered diagonal matrices are the same except for the entries in the first column and first row. The necessary and sufficient condition of solvability is given and some numerical examples are included.

In the paper,we give a class of matrices,that is a srew-idempotent matrix(A2=-A)and present formulas for the rank with respect to srew-idempont matrices.And then obtain equivalent conditions of the sum,the difference and the product of two srew-idempont matrices are srew-idempont matrix.