Interaction entre algèbre linéaire et analyse en formalisation des mathématiques. (Interaction between linear algebra and analysis in formal mathematics)

In this thesis we present the formalization of three principal results that are the Jordan normal form of a matrices, 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.