Eigenvalues, Eigenvectors: Stable Vectorial Planes

This lecture covers the concept of stable vectorial planes, where a function f is given from R³ to R³ along with a subspace V of R³. It discusses the proposition that a vector is an eigenvector of A if and only if it is not a multiple of another vector in V. The lecture also explores the properties of the transpose of A, such as having the same trace, determinant, and characteristic polynomial. Various equations and proofs are presented to illustrate the stability of vectorial planes under the given function.