体上分块矩阵群逆研究

Research on group inverses of block matrices over skew fields

形为M=A BC0矩阵群逆的研究来自一系列从带约束的最优化问题到微分方程的解等众多应用领域的问题.利用分块矩阵运算及矩阵变换的方法,在一定条件下研究了体上M形块阵的群逆问题.给出了2种M形矩阵群逆的存在性定理及相应表示形式,为M形块阵群逆的研究提供了新的思路.

Research on block matrices, whose forms are M =[A B C O], is driven by numerous applied problems ranging from constrained optimization problems to solutions for differential equations. In this paper, block matrix calculation and transforms were used to study the group inverse problems of M type matrices over division rings. The existence theorem and representations of the group inverse for two kinds of M matrices are given, which supplies a new method for examining group inverse problems with M type matrices.