【摘要】 Fm×n表示域F上所有m×n矩阵的集合.R(A)和Nr(A)分别表示矩阵A∈Fm×n的列空间和核空间.若m=n,用Ind(A)定义矩阵A的指标.给出了求一类约束矩阵方程WAWXWBW=D,R(X)R((AW)k1),Nr(X)Nr((WB)k2)的唯一解的Cramer法则,其中A∈Fm×n,W∈Fn×m,B∈Fp×q,W∈Fq×p,D∈Fn×p,R(D)R((WA)k2),Nr(D)Nr((BWk1),k1=Ind(AW),k2=Ind(WA),k1=Ind(BW),k2=Ind(WB).这将[15-17]中的结果从复数域推广到任意域.更多还原

【Abstract】 F m×n be the set of all m×n matrices over a field F.For a matrix A∈F m×n,we denote the column space and right kernel space of A by R（A）and N_r（A）,respectively.If m=n,we also denote by Ind（A）the index of A.A Cramer rule for finding the unique solution of a class of restricted matrix equations WAWX WB W=D,R（X）R（（AW）k₁）,N_r（X）N_r（（WB）k₂）is presented,where A∈F m×n,W∈F n×m,B∈F p×q,W∈F q×p,D∈F n×p,R（D）R（（WA）k₂）,N_r（D）N_r（（B W）k₁）,k₁=Ind（AW）,k₂=Ind（WA）,k₁=Ind（B W）and k₂=Ind（WB）.This generalizes those results in [15,16,17] from the field of complex numbers to any field.更多还原