1.8.13 Quadratic forms
condition: Bring the quadratic form \( f\left(x_{1}, x_{2}\right)=-7 x^{2}+4 x_{1} x_{2}-7 x_{2}^{2} \) \( \mathrm{K} \) to canonical form using methods Lagrange and Jacobi. Determine the sign of a quadratic form.
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.