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Abstract
A symmetric matrix is called copositive if it satisfies the inequality
whenever
and strictly copositive if
, whenever
. The ordering of a vector here is component-wise. Certain interesting properties of the inverse of a copositive matrix are extended to its Moore–Penrose inverse. The inheritance property of the Schur complement of a copositive matrix is extended to the case when the inverses in the Schur complement are replaced by their Moore–Penrose inverses. A framework is provided wherein one has the copositivity of
, given the copositivity of
.
Acknowledgements
The authors thank Rajesh Kannan for discussions concerning Theorem 3.1. They also thank the referee for his/her comments and suggestions, which have resulted in an improved presentation of the work.
Notes
No potential conflict of interest was reported by the authors.