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NP-hardness of polytope M-matrix testing and related problems
In this note we prove NP-hardness of the following problem: Given a set of
matrices, is there a convex combination of those that is a nonsingular
M-matrix? Via known characterizations of M-matrices, our result establishes
NP-hardness of several fundamental problems in systems analysis and control,
such as testing the instability of an uncertain dynamical system, and
minimizing the spectral radius of an affine matrix function