1.8.14 Quadratic Forms
Condition: The quadratic form in a certain basis \ (\ left \ {e_ {1}; e_ {2}; e_ {3} \ right \} \) has the form (q (x) = 2 x_ {1}^{2} +2 x_ {1} x_ {2} - \) \ (-4 x_ {2}^{2} -16 x_ {1} x_ {3} \). Find her matrix in the basis \ (\ left \ {f_ {1} = 4 e_ {1} -e_ {3}; f_ {2} = e_} -2 e_ {2}; f_ {3} = e_ {2} -8 e_} \ right \} \).
Investigation of Quadratic Forms, Their Reduction To Canonical and Normal Forms with Finding Transformation Matrices Using Lagrange and Orthogonal Transformation Methads. Positive and Negative Definite Quadratic Forms, Sylvester's Criterion.