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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access May 15, 2018

Bordering method to compute Core-EP inverse

  • K. Manjunatha Prasad EMAIL logo and M. David Raj
From the journal Special Matrices


Following the work of Kentaro Nomakuchi[10] and Manjunatha Prasad, [7] which relate various generalized inverses of a given matrix with suitable bordering,we describe the explicit bordering required to obtain core-EP inverse, core-EP generalized inverse. The main result of the paper also leads to provide a characterization of Drazin index in terms of bordering.

MSC 2010: 15A09; 15A18


[1] O. M. Baksalary and G. Trenkler. Core inverse of matrices. Linear Multilinear Algebra. 58:681-697, 2010.10.1080/03081080902778222Search in Google Scholar

[2] R. B. Bapat, S. K. Jain, K. M. Prasad and M. D. Raj. Outer inverses: Characterization and applications. Linear Algebra Appl. 528:171-184, 2017.Search in Google Scholar

[3] A. Ben-Israel and T. N. E. Greville. Generalized Inverses: Theory and applications. Springer-Verlag. 2002.Search in Google Scholar

[4] J. W. Blattner. Bordered matrices. J. Soc. Indust. Appl. Math. 10:528-536, 1962.10.1137/0110040Search in Google Scholar

[5] N. Eagambaram. (i, j,..., k)-Inverses via Bordered Matrices. Sankhy¯a: The Indian Journal of Statistics, Series A. 298-308, 1991.Search in Google Scholar

[6] A. J. Goldman and M. Zelen. Weak generalized inverses and minimum variance linear unbiased estimation(Theory of least squares and adaptation to statistical models more complicated than classical presentation). Journal of Research. 68:151-172, 1964.10.6028/jres.068B.021Search in Google Scholar

[7] K.Manjunatha Prasad and K. P. S. Bhaskara Rao. On Bordering of RegularMatrices. Linear Algebra Appl. 234:245-259, 1996.10.1016/0024-3795(94)00116-2Search in Google Scholar

[8] K. Manjunatha Prasad. An introduction to generalized inverse, in: R. B. Bapat, Steve Kirkland, K. Manjunatha Prasad, Simo Puntanen (Eds.), Lectures on Matrix and Graph Methods, Manipal University Press, Manipal, India. Ch. 5, pp. 43-60, 2012.Search in Google Scholar

[9] K. Manjunatha Prasad and K.S. Mohana. Core-EP inverse. Linear Multilinear Algebra. 62:792-802, 2014.10.1080/03081087.2013.791690Search in Google Scholar

[10] K. Nomakuchi. On the characterization of generalized inverses by bordered matrices. Linear Algebra Appl. 33:1-8, 1980.10.1016/0024-3795(80)90093-2Search in Google Scholar

Received: 2018-01-24
Accepted: 2018-03-27
Published Online: 2018-05-15

© 2018, published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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