反三角分块矩阵的群逆存在性和表达式

Existence and representation of group inverse of anti-triangular block matrices

复数域上2×2分块矩阵的Drazin逆的表达式是有待解决的一个公开问题。文章研究了复数域上P+Q群逆的问题,进而利用群逆的定义和给出的条件,研究分块矩阵群逆的存在性和表达式,最后给出了反三角分块矩阵在某些条件下群逆存在的条件。

T he representation for the Drazin inverse of a 2 × 2 block matrix over a complex field is still an open problem .In this paper ,the group inverse problem of P＋ Q in complex fields is researched , the existence and representation of the group inverse of block matrices are derived in light of the defi‐nition of group inverse and the given conditions ,and the conditions of the existence of group inverse of anti‐triangular block matrices under some conditions are worked out .