摘要
给出了复矩阵A的四种Penrose逆A( 1,2 ) ,A( 1,2 ,3) ,A( 1,2 ,4 ) ,A( 1,3,4 ) 的通式 ,它们分别是G =A- r +A- rAu(I -AA- r) + (I-A- rA)uAA- r + (I-A- rA)uAu(I -AA- r) ,G =A- r,l+ (I -A- r ,lA)uAA- r,l,G =A- r,m +A- r ,mAu(I-AA- r,m) ,G =A- l,mAA- l,m + (I-A- l,mA)u(I-AA- l,m) ,其中 ,A- r ∈A{ 1,2 } ,A- r ,l∈A{ 1,2 ,3} ,A- r,m∈A{ 1,2 ,4 } ,A- l,m∈A{ 1,3,4 } 。
The general forms for four kinds of penrose_inverses of a complex matrix are given in this paper, which are as following:G=A\+-\-r+A\+-\-rAu(I-AA\+-\-r)+(I-A\+-\-rA)uAA\+-\-r+(I-A\+-\-rA)uAu(I-AA\+-\-r), G=A - r,l +(I-A - r,l A)uAA - r,l , G=A - r,m +A - r,m Au(I-AA - r,m ), G=A - l,m AA - l,m +(I-A - l,m A)u(I-AA - l,m ),Where, A\+-\-r∈A {1,2}, A - r,l ∈A {1,2,3}, A - r,m ∈A {1,2,4}, A - l,m ∈A {1,3,4}, u is arbitrary matrix.
出处
《曲阜师范大学学报（自然科学版）》
CAS
1996年第1期29-31,共3页
Journal of Qufu Normal University(Natural Science)
