A note on additive results for the Drazin inverse

References

• Bauer , F and Fike , C . 1960 . Norms and exclusion theorem . Numer. Math. , 2 : 137 – 141 .
   Google Scholar
• Ben-Isreal , A and Greville , TNE . 2003 . Generalized Inverses: Theory and Applications, , 2nd , New York : Springer .
   Google Scholar
• Campbell , SL and Meyer , CD . 1979 . Generalized Inverse of Linear Transformations , London : Pitman . SIAM, Philadelphia, 2009
   Google Scholar
• Castro-González , N . 2005 . Additive perturbation results for the Drazin inverse . Linear Algebra Appl. , 397 : 279 – 297 .
   Web of Science ®Google Scholar
• Castro-González , N , Dopazo , E and Martnez-Serrano , MF . 2009 . On the Drazin inverse of the sum of two operators and its application to operator matrices . J. Math. Anal. Appl. , 350 : 207 – 215 .
   Web of Science ®Google Scholar
• Castro-González , N and Koliha , JJ . 2004 . New additive properties of the g-Drazin inverse . Proc. Roy. Soc. Edinb. , 134A : 1085 – 1097 .
   Google Scholar
• Castro-González , N , Koliha , JJ and Rakočević , V . 2002 . Continuity and general perturbation of the Drazin inverse for closed linear operators . Abstr. Appl. Anal. , 7 : 335 – 347 .
   Google Scholar
• Chen , J , Xu , Z and Wei , Y . 2009 . Representations for the Drazin inverse of the sum P + Q + R + S and its applications . Linear Algebra Appl. , 430 : 438 – 454 .
   Web of Science ®Google Scholar
• Cvetković-Ilić , D , Djordjević , D and Wei , Y . 2006 . Additive results for the generalized Drazin inverse in a Banach algebra . Linear Algebra Appl. , 418 : 53 – 61 .
   Web of Science ®Google Scholar
• Deng , C and Du , H . 2006 . The reduced minimum modulus of Drazin inverses of linear operators on Hilbert spaces . Proc. Amer. Math. Soc. , 134 : 3309 – 3317 .
   Web of Science ®Google Scholar
• Deng , C and Wei , Y . 2009 . Characterizations and representations of the Drazin inverse involving idempotents . Linear Algebra Appl. , 431 : 1526 – 1538 .
   Web of Science ®Google Scholar
• Djordjević , D and Wei , Y . 2002 . Additive results for the generalized Drazin inverse . J. Aust. Math. Soc. , 73 : 115 – 125 .
   Web of Science ®Google Scholar
• Drazin , MP . 1958 . Pseudoinverse in associative rings and semigroups . Amer. Math. Monthly , 65 : 506 – 514 .
   Google Scholar
• Eisenstat , SC . 2006 . A perturbation bound for the eigenvalues of a singular diagonalizable matrix . Linear Algebra Appl. , 416 : 742 – 744 .
   Web of Science ®Google Scholar
• Eisensat , SC and Ipsen , ICF . 1998 . Three absolute perturbation bounds for matrix eigenvalues imply relative bounds . SIAM J. Matrix Anal. Appl. , 20 : 149 – 158 .
   Web of Science ®Google Scholar
• Freedman , DZ . 2004 . Perturbation bounds for the joint spectrum of commuting matrices . Linear Algebra Appl. , 387 : 29 – 40 .
   Web of Science ®Google Scholar
• Hartwig , RE and Shoaf , JM . 1977 . Group inverses and Drazin inverses of bidiagonal and triangular Toeplitz matrices . Aust. J. Math. , 24 ( A ) : 10 – 34 .
   Google Scholar
• Hartwig , RE , Wang , G and Wei , Y . 2001 . Some additive results on Drazin inverse . Linear Algebra Appl. , 322 : 207 – 217 .
   Web of Science ®Google Scholar
• Meyer , CD . 1980 . The condition number of a finite Markov chains and perturbation bounded for the limiting probabilities . SIAM J. Algebraic Discrete Methods , 1 : 163 – 181 .
   Web of Science ®Google Scholar
• Meyer , CD and Rose , NJ . 1977 . The index and the Drazin inverse of block triangular matrices . SIAM J. Appl. Math. , 33 : 1 – 7 .
   Web of Science ®Google Scholar
• Pereira , E and Vitória , J . 2001 . Deflation for block eigenvalues of block partitioned matrices with an application to matrix polynomials of commuting matrices . Comput. Math. Appl. , 42 : 1177 – 1188 .
   Web of Science ®Google Scholar
• Prasolov , VV . 1994 . Problems and Theorems in Linear Algebra , Providence , RI : American Mathematical Society .
   Google Scholar
• Sezginer , R and Overton , M . 1990 . The largest singular value of e X A 0 e −X is convex on convex sets of commuting matrices . IEEE Trans. Automat. Control , 35 : 229 – 230 .
   Web of Science ®Google Scholar
• Simeon , B , Fuhrer , C and Rentrop , P . 1993 . The Drazin inverse in multibody system dynamics . Numer. Math. , 64 : 521 – 539 .
   Web of Science ®Google Scholar
• Wei , Y . 1998 . Expressions for the Drazin inverse of a 2 × 2 block matrix . Linear Multilinear Algebra , 45 : 131 – 146 .
   Google Scholar
• Wei , Y and Li , X . 2003 . An improvement on perturbation bounds for the Drazin inverse . Numer. Linear Algebra Appl. , 10 : 563 – 575 .
   Web of Science ®Google Scholar
• Wei , Y , Li , X and Bu , F . 2005 . A perturbation bound of the Drazin inverse of a matrix by separation of simple invariant subspaces . SIAM J. Matrix Anal. Appl. , 27 : 72 – 81 .
   Web of Science ®Google Scholar
• Wei , Y , Li , X , Bu , F and Zhang , F . 2006 . Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices—Application of perturbation theory for simple invariant subspaces . Linear Algebra Appl. , 419 : 765 – 771 .
   Web of Science ®Google Scholar
• Wei , Y and Wang , G . 1997 . The perturbation theory for the Drazin inverse and its applications . Linear Algebra Appl. , 258 : 179 – 186 .
   Web of Science ®Google Scholar
• Wei , Y and Wu , H . 2000 . The perturbation of the Drazin inverse and oblique projection . Appl. Math. Lett. , 13 : 77 – 83 .
   Web of Science ®Google Scholar
• Xu , Q , Song , C and Wei , Y . 2010 . The stable perturbation of the Drazin inverse of the square matrices . SIAM J. Matrix Anal. Appl. , 31 : 1507 – 1520 .
   Web of Science ®Google Scholar
• Zha , H and Zhang , Z . 1997 . Computing the optimal commuting matrix pairs . BIT , 37 : 202 – 220 .
   Web of Science ®Google Scholar