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Gram-Schmidt Calculator

Orthogonalize a set of vectors

Gram-Schmidt Orthogonalization

Vector v₁ (space-separated)
Vector v₂
Vector v₃ (optional)

The Gram-Schmidt process converts a set of linearly independent vectors into an orthonormal basis — vectors that are mutually perpendicular and each have length 1. It is used in linear algebra, QR decomposition, and machine learning.

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