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Gram-Schmidt Orthogonalization Calculator

Transform a set of linearly independent vectors into an orthonormal basis using the Gram-Schmidt process. Essential for QR decomposition, least-squares problems, and numerical linear algebra.

Vector 1 - X Component

Vector 1 - Y Component

Vector 1 - Z Component

Fill in the required fields to see your result.

Linear Algebra

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.

Key differences

	Gram-Schmidt Orthogonalization Calculator	Gram-Schmidt Orthogonalization Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	3	4
Result	First Orthonormal Vector (X)	Second Orthogonal Vector Magnitude (units)
What it does	Transform a set of linearly independent vectors into an orthonormal basis using the Gram-Schmidt process. Essential for QR decomposition, least-squares problems, and numerical linear algebra.	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.