两个幂等矩阵组合的群逆

Two combinations of group inverse idempotent matrix

证明了两个不同的非零幂等矩阵P,Q的组合A=a P+b Q+c PQ+d QP(其中a,b,c,d∈■,a,b≠0),在条件(PQ)n=(QP)n(n≥1,n∈Z)下存在群逆,并且给出其群逆计算公式.

The group inverse of combinations A = a P ＋ b Q ＋ c PQ ＋ d QP,of two nonzero different idempotent matrices P and Q under the condition（ PQ）~n=（ QP）~n is proved,where a,b,c,d ∈ ,a,b ≠ 0. The formulae of its group inverse is also presented.