On Q-Matrices, Centroids and Simplotopes.
Abstract
This paper establishes a necessary condition for a set of spherical (n-1)-simplicies to cover the sphere S superscript (n-1) in R suberscript n. It is shown that the condition is also sufficient when n = 2 but is not so when n > 2. The result can be viewed as a property of Q-matrices, which arise in connection with the linear complementarity problem. It follows from two others also proved here. One is a partitioning theorem for a particular type of convex body known as a simplotope (the cartesian product of two simplices). The other says that the centroid of a suitable defined spherical sector has a positive inner product with each nonzero element of the sector. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1979
- Accession Number
- ADA074959
Entities
People
- Rabe Von Randow
- Richard Cottle
Organizations
- Stanford University