1.8.8 Quadratic Forms
Condition: write out a quadratic form with this matrix \ (a \). Bring it to the canonical appearance, determine the rank, positive and negative indices, depending on the values of the parameter \ (A \). At what values \ (a \) the form is positively determined? \ [A = \ Left (\ Begin {Array} {CCC} 1 & 2 & -1 \\ 2 & A+4 & 2 A -2 \\ -1 & 2 A -2 & 5 AND {ArRYAY} \ 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.