Eigenvalues, Eigenvectors: Stable Vectorial Lines

This lecture introduces the concept of stable vectorial lines under a linear application in R³, defined as subspaces that remain invariant under the application. It covers the stability condition, examples of stable subspaces, and the notion of eigenvectors. The lecture also explores the properties of eigenvectors, their stability under linear transformations, and their relationship with eigenvalues. Additionally, it discusses the determination of stable vectorial lines associated with a given eigenvalue and presents different possibilities for these lines. The lecture concludes with a detailed explanation of the conditions under which a vectorial line is stable under a linear transformation.