Eigenvalues and Eigenvectors: Understanding Linear Applications

This lecture covers the concepts of eigenvalues and eigenvectors, focusing on how to study a linear application, the utility of the characteristic polynomial, and how to define and calculate eigenvalues and eigenvectors. Through examples and calculations, the instructor explains the geometric nature of eigenvectors and demonstrates how to find all the vectors associated with a given eigenvalue. The lecture also explores the concept of eigenspace and discusses how to determine if a matrix has other eigenvalues.