Extended P-pairs Original Research Article

A P-matrix is a square matrix with positive principal minors. We introduce a natural extension of the class of P-matrices, the class of extended P-pairs. A pair {I, M}, for a P-matrix M, is shown to be contained in an extended P-pair iff SMS has an n-step vector for some sign matrix S. Such a matrix M is called extendable, and an example of a P-matrix that is not extendable is given. Applications to the linear complementarity problem are discussed. A polynomial time algorithm to determine if a pair of matrices is an extended P-pair is given.