Geodesic
Extensions of $P$-Property, $R_0$-Property and Semidefinite Linear Complementarity Problems
Yugoslav journal of operations research, Tome 27 (2017) no. 2, p. 135 .

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In this manuscript, we present some new results for the semidefinite linear complementarity problem in the context of three notions for linear transformations, viz., pseudo $w-P$ property, pseudo Jordan $w-P$ property, and pseudo SSM property. Interconnections with the $P_#$-property (proposed recently in the literature) are presented. We also study the $R_#$-property of a linear transformation, extending the rather well known notion of an $R_0$-matrix. In particular, results are presented for the Lyapunov, Stein, and the multiplicative transformations.
Classification : 90C33, 15A09
Keywords: Linear Complementarity Problem, $P$-property, $R$-property, Semidefinite Linear Complementarity Problem, $w-P$ properties, Jordan $w-P$ property, Moore-Penrose Inverse 
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     author = {I. Jeyaraman and Kavita Bisht and K.C. Sivakumar},
     title = {Extensions of $P${-Property,} $R_0${-Property} and {Semidefinite} {Linear} {Complementarity} {Problems}},
     journal = {Yugoslav journal of operations research},
     pages = {135 },
     publisher = {mathdoc},
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     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2017_27_2_a0/}
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I. Jeyaraman; Kavita Bisht; K.C. Sivakumar. Extensions of $P$-Property, $R_0$-Property and Semidefinite Linear Complementarity Problems. Yugoslav journal of operations research, Tome 27 (2017) no. 2, p. 135 . http://geodesic.mathdoc.fr/item/YJOR_2017_27_2_a0/