Continuity of the Polytope Generated by a Set of Matrices

摘要

Continuity of the polytope generated by a set of matrices is dealt with in this paper. We have defined a norm for the polytope, and verified when these matrices belong to a compact set in R~(n×n) the norm is bounded and the polytope is compact. Moreover, we have verified if the polytope is treated as a set-valued mapping from R~n to R~n, it is continuous and with convex and compact values.