Solving a kind of restricted matrix equations and Cramer rule

The core inverse and constrained matrix approximation problem

“…In [29], Ben-Israel gets a Cramer's rule for obtaining the least-norm solution of the consistent linear system (1.2), . More details of Cramer's rules for finding restricted solutions of (1.2) can be found in [1,3,[31][32][33][34][35][36]. In Theorems 3.4 and 3.6, we will give two Cramer's rules for the unique solution of (1.3).…”

Minimal properties of the Drazin-inverse solution of a matrix equation

“…We assume that A, B, G ∈ C n×n are given matrices. It is shown that the matrix X = A D GB D is the unique solution of the restricted matrix equation (see [14]) AXB = G, where R(G) ⊂ R(A k 1 ), N(B k 2 ) ⊂ N(G), k 1 = ind(A), k 2 = ind(B).…”

“…Taking into account its importance many computational techniques were developed. The Cramer's rules derived for general restricted linear equation [3], as well for restricted matrix equation [4], were generalized for computing the Drazin-inverse solution of a restricted matrix equation in [14]. However, more common problem in the literature is to find a solution of the system…”

Rank constrained matrix best approximation problem

“…In [24], of Cramer's rules for finding restricted solutions of (1.2) can be found in [4,12,13,14,15,25,26]. In the following Theorem 3.4 and Theorem 3.6, we will give two Cramer's rules for the unique solution of (1.3).…”

“…In [24], Wang gives a Cramer's rule for the unique solution x ∈ R M k of (1. and Ind(M ) = k. Furthermore, in [11], Ji obtains a new condensed Cramer's rule of Werner for minimal-norm least-squares solution of (1.2). More details of Cramer's rules for finding restricted solutions of (1.2) can be found in [4,12,13,14,15,25,26]. In the following Theorem 3.4 and Theorem 3.6, we will give two Cramer's rules for the unique solution of (1.3).…”