Complex Eigenvalues and Diagonalizability

This lecture covers the fundamental theorem of algebra, stating that a polynomial with complex coefficients can be factored into linear factors. It also discusses the criterion for diagonalizability of a linear transformation in a complex vector space. The lecture further explores questions related to diagonalizable matrices and the properties of matrices with the same eigenvectors. The instructor emphasizes the importance of understanding complex eigenvalues and their role in determining the diagonalizability of matrices.