Interaction entre algèbre linéaire et analyse en formalisation des mathématiques

Guillaume Cano 1
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this thesis we present the formalization of three principal results that are the Jordan normal form of a matrix, the Bolzano-Weierstraß theorem, and the Perron-Frobenius theorem. To formalize the Jordan normal form, we introduce many concepts of linear algebra like block diagonal matrices, companion matrices, invariant factors, ... The formalization of Bolzano-Weierstraß theorem needs to develop some theory about topological space and metric space. The Perron-Frobenius theorem is not completly formalized. The proof of this theorem uses both algebraic and topological results. We will show how we reuse the previous results.
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Guillaume Cano. Interaction entre algèbre linéaire et analyse en formalisation des mathématiques. Autre [cs.OH]. Université Nice Sophia Antipolis, 2014. Français. ⟨NNT : 2014NICE4016⟩. ⟨tel-00986283⟩

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