1.8 Quadratic Forms
Condition: quadratic form \ (f (x) = x^{t} a x \) bring to the canonical species \ (f (y) = y^{t} a y \). Find the matrix \ (c \) transformation \ (x = c y \), which leads \ (f (x) \) to the species \ (f (y) \). \ [F (x) = x_ {1}^{2} -2 x_ {1} x_ {2} -2 x_ {1} x_ {3} +3 x_ {2}^{2} -2 x_ {2} x_ {3} +2 x_ {3} \ text {. } \]
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.