ALAMT  Vol.2 No.1 , March 2012
Schur Complement of con-s-k-EP Matrices
ABSTRACT
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.

Cite this paper
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.
References
[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.

 
 
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