On extension of Cramer's rule for solutions to restricted matrix equations
Guorong Wang · Journal of Lanzhou University · 2006
The Cramer rules for finding the solutions to X of the restricted matrix equations AX = D, (R(X) (?) R(Ak1)), XB = D, (N(X) (?)N(Bk2)), AXB = D, (R(X) (?) R(Ak1), N(X) (?) N(Bk2)) are presented, where A ∈ Cn×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 Cramer rule is also a special case of our results.