1.8.11 Quadratic forms
Condition: Convert the quadratic form to normal form \[ 2 x_{1}^{2}+2 x_{2}^{2}+2 x_{3}^{2}+2 x_{1} x_{2}+2 x_{2} x_{3}+2 x_{3} x_{1} \text {. } \]
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.