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.