Diagonalization: Step by Step

This lecture covers the process of diagonalization for a linear transformation on a finite-dimensional vector space, including calculating the characteristic polynomial, determining diagonalizability, finding eigenvalues and eigenvectors, and constructing the diagonal matrix. The instructor explains how to factorize the characteristic polynomial, identify real roots, determine algebraic and geometric multiplicities, and find eigenspaces. Emphasis is placed on understanding the steps involved in diagonalization and the significance of eigenvalues and eigenvectors in the process.