1.8.12 Quadratic forms
Condition: Investigate the sign definiteness of the quadratic form depending on the value of the parameter \( \lambda \). \[ f(x, y)=2 \lambda x^{2}+(2 \lambda+8) x y+(\lambda+1) y^{2} \]
Investigation of quadratic forms, their reduction to canonical and normal forms with finding transformation matrices using Lagrange and orthogonal transformation methods. Positive and negative definite quadratic forms, Sylvester's criterion.