Reconstructing a matrix from a partial sampling of Pareto eigenvalues

AbstractLet Λ={λ1,…,λp} be a given set of distinct real numbers. This work deals with the problem of constructing a real matrix A of order n such that each element of Λ is a Pareto eigenvalue of A, that is to say, for all k∈{1,…,p} the complementarity system $$x\geq \mathbf{0}_n,\quad Ax-\lambda_k x\geq \mathbf{0}_n,\quad \langle x, Ax-\lambda_k x\rangle = 0$$ admits a nonzero solution x∈ℝn.

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