Abstract
We give several characterizations of regularity of interval matrices. All of them have to do with solvability of certain systems of nonlinear equations or inequalities. The most illustrative of them is the following one: an interval matrix [A c − Δ, A c + Δ] is regular if and only if the nonlinear inequality \(|x| > \Delta |A_{c}^{-1}x|\) has a solution in each orthant. These results are then applied to derive two theorems of the alternatives for inequalities with absolute values.
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Dedicated to Professor Miroslav Fiedler on the occasion of his 80th birthday
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Rohn, J. Regularity of Interval Matrices and Theorems of the Alternatives. Reliable Comput 12, 99–105 (2006). https://doi.org/10.1007/s11155-006-4877-z
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DOI: https://doi.org/10.1007/s11155-006-4877-z