Schur Complement of con-s-k-EP Matrices

Affiliation(s)

Ramanujan Research Centre, Department of Mathematics, Government Arts College (Autonomous), Kumbakonam, India.

Ramanujan Research Centre, Department of Mathematics, Government Arts College (Autonomous), Kumbakonam, India.

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.

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.

B. Muthugobal, "Schur Complement of con-s-k-EP Matrices,"

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.

[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.