Extended P-pairs

✍ Scribed by Walter D. Morris Jr.

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 558 KB
• Volume: 257
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)00167-x

✦ Synopsis

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.