Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 60, 2012 - Issue 8
Submit an article Journal homepage
203
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

A dominance notion for singular matrices with applications to nonnegative generalized inverses

Debasisha Mishra Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India
&
K.C. Sivakumar Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, IndiaCorrespondence[email protected]
Pages 911-920 | Received 11 Apr 2011, Accepted 11 Oct 2011, Published online: 25 Nov 2011

References

  • Argyros , IK and Szidarovszky , F . 1993 . The Theory and Applications of Iteration Methods , Boca Raton, FL : Systems Engineering Series, CRC Press .
  • Ben-Israel , A and Greville , TNE . 2003 . Generalized inverses: Theory and Applications , New York : Springer-Verlag .
  • Berman , A and Neumann , M . 1976 . Proper splittings of rectangular matrices . SIAM J. Appl. Math. , 31 : 307 – 312 .
  • Berman , A and Plemmons , RJ . 1974 . Cones and iterative methods for best square least squares solutions of linear systems . SIAM J. Numer. Anal. , 11 : 145 – 154 .
  • Berman , A and Plemmons , RJ . 1974 . Matrix group monotonicity . Proc. Am. Math. Soc. , 46 : 355 – 359 .
  • Berman , A and Plemmons , RJ . 1994 . Nonnegative Matrices in the Mathematical Sciences , Philadelphia : SIAM .
  • Collatz , L . 1966 . Functional Analysis and Numerical Mathematics , New York : Academic .
  • Desoer , CA and Whalen , BH . 1963 . A note on pseudoinverses . J. Soc. Ind. Appl. Math. , 11 : 442 – 447 .
  • Hanke , M and Neumann , M . 1990 . Preconditionings and splittings for rectangular systems . Numer. Math. , 57 : 85 – 93 .
  • Kuo , I . 1977 . The Moore–Penrose inverses of singular M-matrices . Linear Algebra Appl. , 17 : 1 – 14 .
  • Mangasarian , OL . 1968 . Characterization of real matrices of monotone kind . SIAM Rev. , 10 : 439 – 441 .
  • Pye , WC . 1980 . Nonnegative Drazin inverses . Linear Algebra Appl. , 30 : 149 – 153 .
  • Seneta , E . 2006 . Nonnegative Matrices and Markov Chains , New York : Springer .
  • Szidarovszky , F and Okuguchi , K . 1990 . A general scheme for matrices with nonnegative inverse . PUMA , 1 : 109 – 114 . Ser. B
  • Wei , Y . 1998 . Index splitting for the Drazin inverse and the singular linear system . Appl. Math. Comput. , 95 : 115 – 124 .
  • Wei , Y and Wu , H . 2001 . Additional results on index splittings for Drazin inverse solutions of singular linear systems . Electron. J. Linear Algebra , 8 : 83 – 93 .
  • Wei , Y and Wu , H . 2001 . (T, S) splitting methods for computing the generalized inverse and rectangular systems . Int. J. Comput. Math. , 77 ( 3 ) : 401 – 424 .
  • Varga , RS . 2000 . Matrix Iterative Analysis , Berlin : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.