Bernik, J., Drnovsek, R., Kosir, T., Laffey, T., MacDonald, G. W., Meshulam, R., … Radjavi, H. (2005). Common fixed points and common eigenvectors for sets of matrices. Linear & Multilinear Algebra, 53(2), 137-146.

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Common fixed points and common eigenvectors for sets of matrices

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 Show moreThe 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. Show less