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Maximal Lower Bounds in the Loewner order


We show that the set of maximal lower bounds of two symmetric matrices with respect to Loewner order can be identified to the quotient set O(p,q)/(O(p)×O(q)). Here, (p,q)denotes the inertia of the difference of the two matrices, O(p) is the p-th orthogonal group, and O(p,q) is the indefinite orthogonal group arising from a quadratic form with inertia (p,q). We discuss the application of this result to the synthesis of ellipsoidal invariants of hybrid dynamical systems.
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hal-01263476 , version 1 (27-01-2016)


  • HAL Id : hal-01263476 , version 1


Nikolas Stott, Xavier Allamigeon, Stéphane Gaubert. Maximal Lower Bounds in the Loewner order. 2015 SIAM Conference on Applied Linear Algebra, Oct 2015, Atlanta, United States. ⟨hal-01263476⟩
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