Diagonalization in Symmetric Matrices

This lecture covers the process of diagonalizing symmetric matrices in an orthonormal basis, starting with finding eigenvalues and eigenvectors, ensuring orthogonality, and normalizing the vectors. The instructor explains the advantages of diagonalizing symmetric matrices, emphasizing the importance of orthogonality and the ease of transposition compared to inversion. The lecture delves into the conditions for diagonalizability, highlighting the significance of symmetric matrices in this process. The concept of orthonormal bases is explored, showcasing the benefits of having orthogonal vectors and the implications for matrix operations. The lecture concludes with a detailed explanation of the properties and applications of diagonalization in symmetric matrices.