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Quadratic Form Calculator

Evaluate a quadratic form Q(x) = x^T A x for a symmetric 2×2 matrix and a vector (x₁, x₂). Use it to test whether a matrix is positive definite, negative definite, or indefinite.

Matrix element (1,1)

Matrix element (1,2)

Matrix element (2,2)

Variable x₁

Variable x₂

Fill in the required fields to see your result.

Linear Algebra

Quadratic Form Calculator

Evaluate a 2-variable quadratic form Q(x₁, x₂) and analyze its definiteness. Useful in optimization, geometry, and studying conic sections.

Coefficient a₁₁

Coefficient a₁₂

Coefficient a₂₂

Variable x₁ value

Variable x₂ value

Fill in the required fields to see your result.

Key differences

	Quadratic Form Calculator	Quadratic Form Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	5	5
Result	Quadratic Form Value	Quadratic Form Value
What it does	Evaluate a quadratic form Q(x) = x^T A x for a symmetric 2×2 matrix and a vector (x₁, x₂). Use it to test whether a matrix is positive definite, negative definite, or indefinite.	Evaluate a 2-variable quadratic form Q(x₁, x₂) and analyze its definiteness. Useful in optimization, geometry, and studying conic sections.