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Both calculators run independently — change the inputs on either side to compare results.

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

2x2 Matrix Determinant Calculator

Compute the determinant of any 2×2, 3×3, or 4×4 square matrix instantly. Use it to check invertibility, solve linear systems, or evaluate transformations in linear algebra.

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	2x2 Matrix Determinant Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	5	4
Result	Quadratic Form Value	Determinant
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.	Compute the determinant of any 2×2, 3×3, or 4×4 square matrix instantly. Use it to check invertibility, solve linear systems, or evaluate transformations in linear algebra.