Common fixed points and common eigenvectors for sets ...



Title Common fixed points and common eigenvectors for sets of matrices
Author(s) J. Bernik, R. Drnovsek, T. Kosir, T. Laffey, Gordon W. MacDonald, R. Meshulam, M. Omladic, H. Radjavi
Journal Linear & Multilinear Algebra
Date 2005
Volume 53
Issue 2
Start page 137
End page 146
Abstract The following questions are studied: Under what conditions does the existence of a (nonzero) fixed point for every member of a semigroup of matrices imply a common fixed point for the entire semigroup? What is the smallest number k such that the existence of a common fixed point for every k members of a semigroup implies the same for the semigroup? If every member has a fixed space of dimension at least k: What is the best that can be said about the common fixed space? We also consider analogs of these questions with general eigenspaces replacing fixed spaces.

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