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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

Matrix Inverse Calculator

Find the inverse of a 2×2 or 3×3 matrix instantly. Use this when solving systems of linear equations, transforming coordinates, or working through linear algebra coursework.

Element (1,1)

Element (1,2)

Element (2,1)

Element (2,2)

Fill in the required fields to see your result.

Key differences

	Quadratic Form Calculator	Matrix Inverse Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	5	4
Result	Quadratic Form Value	Inverse Element (1,1)
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.	Find the inverse of a 2×2 or 3×3 matrix instantly. Use this when solving systems of linear equations, transforming coordinates, or working through linear algebra coursework.