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|
|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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