Geodesic
Note on the core matrix partial ordering
Discussiones Mathematicae. Probability and Statistics, Tome 31 (2011) no. 1-2, pp. 71-75.

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Complementing the work of Baksalary and Trenkler [2], we announce some results characterizing the core matrix partial ordering.
Keywords: core inverse, core partial ordering, generalized inverse, group inverse, left star partial ordering, minus partial ordering, Moore-Penrose inverse, right sharp partial ordering 
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Mielniczuk, Jacek. Note on the core matrix partial ordering. Discussiones Mathematicae. Probability and Statistics, Tome 31 (2011) no. 1-2, pp. 71-75. http://geodesic.mathdoc.fr/item/DMPS_2011_31_1-2_a4/

[1] J.K. Baksalary and S.K. Mitra, Left-star and right-star partial orderings, Linear Algebra Applications 149 (1991) 73-89.

[2] O.M. Baksalary and G. Trenkler, Core inverse of matrices, Linear and Multilinear Algebra 58 (2010) 681-697.

[3] D.S. Bernstein, Matrix Mathematics: Theory, Facts and Formulas (Princeton University Press, 2009).

[4] S.K. Mitra, P. Bhimasankaram and S.B. Malik, Matrix Partial Orders, Shorted Operators and Applications (World Scientific, 2010).

[5] C.R. Rao and S.K. Mitra, Generalized Inverse of Matrices and its Applications (Wiley, 1971).