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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

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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

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Key differences

	Gram-Schmidt Orthogonalization Calculator	Gram-Schmidt Orthogonalization
Category	Linear Algebra	Linear Algebra
Inputs required	3	5
Result	First Orthonormal Vector (X)	Orthogonalization Result
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 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.