Abstract
In this article, we study the properties of some matrix classes using principal pivot transform (PPT). These matrices with some additional conditions have nonnegative principal minors. We show that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with \(Q_{0}\)-property is captured by sufficient matrices introduced by Cottle et al. in (Linear Algebra Appl 114/115:231–249 1989) and the solution set of a linear complementarity problem is the same as the set of Karush–Kuhn–Tucker stationary points of the corresponding quadratic programming problem. We introduce some more PPT based matrix classes in continuation of (Linear Algebra Appl 400:243–252 2005) and study the properties of these classes.
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Acknowledgments
This work is carried out under the project on Optimization and Reliability Modelling of Indian Statistical Institute. The author wishes to thank the unknown referees who have patiently gone through the article and whose suggestions have considerably improved its presentation and readability.
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Das, A.K. Properties of some matrix classes based on principal pivot transform. Ann Oper Res 243, 375–382 (2016). https://doi.org/10.1007/s10479-014-1622-6
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DOI: https://doi.org/10.1007/s10479-014-1622-6