1.8.15 Quadratic Forms
Condition: Give a quadratic form \ (Q \ Left (X_ {1}, X_ {2}, X_ {3} \ RIGHT) \) to canonical species (bringing to the main axes). \[ \begin{array}{l} q\left(x_{1}, x_{2}, x_{3}\right)=x_{1}^{2}-5 x_{2}^{2}+x_{3}^{2}+4 x_{1} x_ {2} +2 x_ {1} x_ {3}+\\ +4 x_ {2} x_ {3}. \ end {Array} \]
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.