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Gram-Schmidt Orthogonalization Calculator

Convert two linearly independent 2D vectors into an orthonormal basis using the Gram-Schmidt process. Ideal for linear algebra students working on QR decomposition, subspace projections, or eigenvalue problems.

Vector 1 - x component

Vector 1 - y component

Vector 2 - x component

Vector 2 - y component

Fill in the required fields to see your result.

Linear Algebra

Gram-Schmidt Orthogonalization

Convert a set of linearly independent 2D vectors into a mutually orthogonal (or orthonormal) basis using the Gram-Schmidt process. Used in linear algebra, QR decomposition, and numerical methods courses.

Vector 1 - X Component

Vector 1 - Y Component

Vector 2 - X Component

Vector 2 - Y Component

Process Step

Fill in the required fields to see your result.

Key differences

	Gram-Schmidt Orthogonalization Calculator	Gram-Schmidt Orthogonalization
Category	Linear Algebra	Linear Algebra
Inputs required	4	5
Result	Second Orthogonal Vector Magnitude (units)	Orthogonalization Result
What it does	Convert two linearly independent 2D vectors into an orthonormal basis using the Gram-Schmidt process. Ideal for linear algebra students working on QR decomposition, subspace projections, or eigenvalue problems.	Convert a set of linearly independent 2D vectors into a mutually orthogonal (or orthonormal) basis using the Gram-Schmidt process. Used in linear algebra, QR decomposition, and numerical methods courses.