Quadratic Forms and Symmetric Matrices

This lecture explores examples of algebraic quotients by looking at quadratic forms with the action of SLN and the special orthogonal group. The instructor demonstrates how to find the quotient using invariance maps and the discriminant, showing that the affine line over C is normal. The lecture also covers the diagonalizability of symmetric matrices with different eigenvalues and concludes by applying the quotient criterion to deduce that Cn is the quotient, emphasizing the importance of normality in these algebraic structures.