矩阵和的Drazin逆表示的新结果
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摘要
<正>1引言设C~(m×n)表示m×n复矩阵的集合,rank(A)表示矩阵A的秩,对于A∈C~(m×n),使得rank(A~k)=rank(A~(k+1))成立的最小正整数k称为A的指标,记作ind(A).设ind(A)=κ,满足A~(k+1)X=A~k,XAX=X,AX=XA的矩阵X称为矩阵A的Drazin逆,记为A~D.若ind(A)=1,则A~D称为A的群逆,记
In this paper,new formulas for the Drazin inverse of the sum of two matrices are given under some conditions which are more general than those used in some current literature.Then,according to ideas of the matrix decomposition and matrix splitting,using the theory of Drazin inverse,new representation of partitioned matrices M=■ is given under some conditions.
In this paper,new formulas for the Drazin inverse of the sum of two matrices are given under some conditions which are more general than those used in some current literature.Then,according to ideas of the matrix decomposition and matrix splitting,using the theory of Drazin inverse,new representation of partitioned matrices M=■ is given under some conditions.
引文
[1]Ben-Israel A and Greville T N E.Generalized Inverses:Theory and Applications,SpringerVerlag,New York,2003.
[2]Campbell S L.Singular Systems of Differential Equations.Pitman,London,1980.
[3]Hartwig R E,Wang G R and Wei Y M.Some additive results on Drazin inverse.Linear Algebra Appl.,2001,322:207-217.
[4]Shakoor A,Yang H and Ali I.The Drazin inverses of the sum of two matrices and block matrix.J.Appl.Math.Inform.,2013,31:343-352.
[5]白淑艳.体上两个矩阵和的Drazin逆表达式及其应用.哈尔滨工程大学,2012.
[6]Patricio P and Hartwig R E.Some additive results on Drazin inverses.Appl.Math.Comput.,2009,215:530-538.
[7]Yang H and Liu X F.The Drazin inverse of the sum of two matrices and its applications.J.Comput.Appl.Math.,2011,235:1412-1417.
[8]Hartwig R,Li X Z and Wei Y M.Representations for the Drazin inverse of a 2 x 2 block matrix.SIAM J.Matrix Anal.Appl.,2005,27(3):757-771.
[9]林荣珍,江飞.3-幂零矩阵的相似等价类的计数.数学研究,2006,39(4):394-400.
[10]Martinez-Serrano M F and Castro-González N.On the Drazin inverse of block matrices and generalized Schur complement.Appl.Math.Comput.,2009,215:2733-2740.
[11]Liu X F and Yang H.Further results on the group inverses and Drazin inverses of anti-triangular block matrices.Appl.Math.Comput.,2012,218:8978-8986.
[12]曹重光.体上分块矩阵群逆的某些结果.黑龙江大学自然科学学报,2001,18(3):5-7.
[13]Miao J.Results of the Drazin inverse of block matrices.J.Shanghai Normal Univ.,1989,18:25-31.
[2]Campbell S L.Singular Systems of Differential Equations.Pitman,London,1980.
[3]Hartwig R E,Wang G R and Wei Y M.Some additive results on Drazin inverse.Linear Algebra Appl.,2001,322:207-217.
[4]Shakoor A,Yang H and Ali I.The Drazin inverses of the sum of two matrices and block matrix.J.Appl.Math.Inform.,2013,31:343-352.
[5]白淑艳.体上两个矩阵和的Drazin逆表达式及其应用.哈尔滨工程大学,2012.
[6]Patricio P and Hartwig R E.Some additive results on Drazin inverses.Appl.Math.Comput.,2009,215:530-538.
[7]Yang H and Liu X F.The Drazin inverse of the sum of two matrices and its applications.J.Comput.Appl.Math.,2011,235:1412-1417.
[8]Hartwig R,Li X Z and Wei Y M.Representations for the Drazin inverse of a 2 x 2 block matrix.SIAM J.Matrix Anal.Appl.,2005,27(3):757-771.
[9]林荣珍,江飞.3-幂零矩阵的相似等价类的计数.数学研究,2006,39(4):394-400.
[10]Martinez-Serrano M F and Castro-González N.On the Drazin inverse of block matrices and generalized Schur complement.Appl.Math.Comput.,2009,215:2733-2740.
[11]Liu X F and Yang H.Further results on the group inverses and Drazin inverses of anti-triangular block matrices.Appl.Math.Comput.,2012,218:8978-8986.
[12]曹重光.体上分块矩阵群逆的某些结果.黑龙江大学自然科学学报,2001,18(3):5-7.
[13]Miao J.Results of the Drazin inverse of block matrices.J.Shanghai Normal Univ.,1989,18:25-31.