Abstract
This paper contributes several new results on core matrices by presenting some characterizations involving c-inverses. Some relations to matrix partial orders are shown as well.
Similar content being viewed by others
References
O.M. Baksalary, G.P.H. Styan and G. Trenkler, On a matrix decomposition of Hartwig and Spindelböck, Linear Algebra Appl., 430 (2009), 2798–2812.
A. Ben-Israel and T.N.E. Greville, Generalized Inverses: Theory and Applications, Springer-Verlag, New York (2003).
J. Benitez, X. Liu and J. Zhong, Some results on matrix partial orderings and reverse order law, Electron. J. Linear Algebra, 20 (2010), 254–273.
C. Cao, X. Zhang and X. Tang, Reverse order law of group inverses of products of two matrices, Appl. Math. Comput., 158 (2004), 489–495.
M. Eagambaram, M.K. Prasad and K.S. Mohana, Column space decomposition and partial order on matrices, Electron. J. Linear Algebra, 26 (2013), 795–815.
J. Groß, Remarks on the sharp partial order and the ordering of squares of matrices, Linear Algebra Appl., 417 (2006), 87–93.
R.E. Hartwig, How to partially order regular elements, Math. Japon., 25 (1980), 1–13.
S.K. Mitra, The minus partial order and the shorted matrix, Linear Algebra Appl., 83 (1986), 1–27.
S.K. Mitra, On group inverses and the sharp order, Linear Algebra Appl., 92 (1987), 17–37.
S.K. Mitra, Shorted matrices in star and related orderings, Circuits Systems Signal Process., 9 (1990), 197–212.
S.K. Mitra, P. Bhimasankaram and S.B. Malik, Matrix Partial Orders, Shorted Operators and Applications, World Scientific, Singapore (2010).
K.S.S. Nambooripad, The natural partial order on a regular semigroup, Proc. Edinburgh Math. Soc., 23 (1980), 249–260.
C.R. Rao and S.K. Mitra, Generalized Inverse of Matrices and its Applications, Wiley, New York (1971).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mielniczuk, J. Some results on C-inverses of a core matrix. Indian J Pure Appl Math 46, 383–395 (2015). https://doi.org/10.1007/s13226-015-0122-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-015-0122-y