1.8.16 Quadratic forms
condition: Reduce the quadratic form to canonical form using the Lagrange method. \[ x_{1}^{2}+4 x_{1} x_{2}+2 x_{1} x_{3}+3 x_{2}^{2}+2 x_{2} x_{3}+x_{3}^{2} \text {. } \]
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.