Classification of Quadratic Forms

This lecture covers the classification of quadratic forms using orthogonal diagonalization of symmetric matrices. It explains the concepts of positive definite, negative definite, and non-definite quadratic forms, along with their relation to eigenvalues. The instructor demonstrates how to determine the definiteness of a quadratic form based on the signs of eigenvalues. Various examples are provided to illustrate the classification process, emphasizing the importance of orthogonal diagonalization in analyzing quadratic forms.