Schur Complement of con-s-k-EP Matrices

DOI: 10.4236/alamt.2012.21001   PDF   HTML     5,411 Downloads   15,598 Views   Citations


Necessary and sufficient conditions for a schur complement of a con-s-k-EP matrix to be con-s-k-EP are determined. Further it is shown that in a con-s-k-EPr matrix, every secondary sub matrix of rank “r” is con-s-k-EPr. We have also discussed the way of expressing a matrix of rank r as a product of con-s-k-EPr matrices. Necessary and sufficient conditions for products of con-s-k-EPr partitioned matrices to be con-s-k-EPr are given.

Share and Cite:

B. Muthugobal, "Schur Complement of con-s-k-EP Matrices," Advances in Linear Algebra & Matrix Theory, Vol. 2 No. 1, 2012, pp. 1-11. doi: 10.4236/alamt.2012.21001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Krishnamoorthy, K. Gunasekaran and B. K. N. Muthugobal, “con-s-k-EP Matries,” Journal of Mathematical Sciences and Engineering Applications, Vol. 5, No. 1, 2011, pp. .
[2] C. R. Rao and S. K. Mitra, “Generalized Inverse of Matrices and Its Applications,” Wiley and Sons, New York, 1971.
[3] R. Pe-nrose, “On Best Approximate Solutions of Linear Matrix Equa-tions,” Mathematical Proceedings of the Cambridge Philo-sophical Society, Vol. 52, No. 1, 1959, pp. 17-19.
[4] T. S. Baskett and I. J. Katz, “Theorems on Products of EPr Matrices,” Linear Algebra and Its Applications, Vol. 2, No. 1, 1969, pp. 87-103.
[5] A. R. Meenakshi, “On Schur Complements in an EP Matrix, Periodica, Mathematica Hungarica,” Periodica Mathematica Hungarica, Vol. 16, No. 3, 1985, pp. 193- 200.
[6] D. H. Carlson, E. Haynesworth and T. H. Markham, “A Generalization of the Schur Complement by Means of the Moore-Penrose Inverse,” SIAM Journal on Applied Ma- the-matics, Vol. 26, No. 1, 1974, pp. 169-175.
[7] A. B. Isral and T. N. E. Greviue, “Generalized Inverses Theory and Applica-tions,” Wiley and Sons, New York, 1974.
[8] S. Krishna-moorthy, K. Gunasekaran and B. K. N. Muthugobal, “On Sums of con-s-k-EP Matrix,” Thai Journal of Mathematics.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.