Diagonalisable Matrices and Linear Transformations

This lecture covers the concept of diagonalizability for linear transformations in finite-dimensional vector spaces. It explains how a transformation is considered diagonalizable if it has a basis of eigenvectors. The lecture also discusses diagonalizable matrices and their similarity to diagonal matrices. Additionally, it explores the conditions under which a linear transformation or a matrix is diagonalizable, based on the number of distinct eigenvalues. The instructor presents examples to illustrate the concepts, emphasizing the importance of eigenvectors and eigenvalues in determining diagonalizability.