Gram-Schmidt Calculator (2D)
The Gram-Schmidt Calculator turns two 2D vectors into an orthogonal (and orthonormal) basis using the Gram-Schmidt process. Enter the components of both vectors.
Formula
u₁ = v₁; u₂ = v₂ − (v₂·u₁ / u₁·u₁) u₁; then normalise
- The process removes from v₂ its component along u₁, leaving an orthogonal vector.
- Dividing each by its length gives an orthonormal basis.
v₁ = (3,1), v₂ = (2,2)
Inputs
- v₁ x: 3
- v₁ y: 1
- v₂ x: 2
- v₂ y: 2
u₂ = (2,2) − (8/10)(3,1) = (−0.4, 1.2), orthogonal to u₁.
Frequently asked questions
What is Gram-Schmidt used for?
It converts any independent set of vectors into an orthogonal or orthonormal basis, used widely in QR decomposition.