The group inverse of some special block matrices
Jiemei Zhao · Harbin Gongcheng Daxue Xuebao/Journal of Harbin Engineering University · 2009
Generalized inverses of block matrices are very useful in mathematical theory.They can also be applied in practices ranging from automated control systems,systems theory,probability statistics,mathematical programming and so on.Expressions for the group inverses of block matrices in the form of [ABC0] were studied.Let P be an idempotent matrix over the field of complex numbers and matrices A,B,C be in the set {P,PP*,PP*P },we get 27 classes of block matrices in the form of [ABC0].This paper gives the existence conditions and the expressions for the group inverses of the 27 classes of block matrices.