Eigenvalues and Eigenvectors: General Definition and Examples

This lecture continues the discussion on eigenvalues and eigenvectors, emphasizing the importance of understanding these concepts. The instructor revisits the general definition of eigenvalues and provides various examples to illustrate how to find them. Special cases, such as the identity transformation and the zero transformation, are explored. The lecture also covers the concept of eigenspaces and clarifies the distinction between eigenvectors and the zero vector. Examples include transformations like the identity, zero, and orthogonal projections. The lecture concludes with a detailed explanation of diagonalizable transformations and their significance in linear algebra.