一类约束矩阵方程解的Cramer法则(英文)

On extension of Cramer's rule for solutions to restricted matrix equations

证明了一类约束矩阵方程 AX=D,(R(X)(?) R(Ak1)), XB=D,(N(X)(?) N(Bk2)), AXB=D,(R(X)(?) R(Ak2),N(X)(?)N(Bk2)) 有唯一解并给出其解的Cramer公式,其中A∈Cn×n,Ind(A)=k1,B∈Cm×m,Ind(B)=k2,D∈ Cn×m．推广了求解约束线性方程组问题中的相关结论．经典的Cramer法则也是本文结论的特殊情形．

The Cramer rules for finding the solutions to X of the restricted matrix equations AX=D,（R（X）belong to R（A^k1））, XB=N（B^k2））belong to D,（N（X） AXB=D,（R（X）belong to R（A^k1）,N（B^k2）belong to N（X） are presented, where A ∈ C^n×n with Ind（A） = k1, B ∈ Cm×m with Ind（B） = k2, and D∈Cn^×m. The results in this paper can be considered as the extension of some results concerning linear systems. The classical Crarner rule is also a special case of our results.