Math Problem Statement

Show that the matrix for the following quadratic form is positive definite 3x21

  • 2x22 − 2 √ 2 x1x2

Solution

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Math Problem Analysis

Mathematical Concepts

Quadratic Forms
Matrix Algebra
Positive Definiteness

Formulas

Quadratic form Q(x) = x^T A x
Determinant of a 2x2 matrix: det(A) = ad - bc

Theorems

Sylvester's Criterion
Properties of Positive Definite Matrices

Suitable Grade Level

University level (Linear Algebra)