Linear Algebra: Canonical Basis

This lecture covers the concept of a canonical basis in linear algebra, focusing on the representation of matrices in different bases, the verification of bases, and the diagonalizability of matrices. The instructor explains the process of finding bases that satisfy specific conditions and demonstrates how to determine if a matrix is diagonalizable. The lecture also delves into characteristic polynomials, eigenvectors, and eigenvalues, illustrating how they relate to the diagonalizability of matrices.