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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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Linear Algebra

Gram-Schmidt Process Calculator

Transform a set of linearly independent vectors into an orthogonal or orthonormal basis using the Gram-Schmidt process. Useful in linear algebra courses, QR decomposition, and signal processing applications.

Normalization

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	Gram-Schmidt Process Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	5	5
Result	Orthogonalization Result	First Orthogonal Vector Magnitude
What it does	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.	Transform a set of linearly independent vectors into an orthogonal or orthonormal basis using the Gram-Schmidt process. Useful in linear algebra courses, QR decomposition, and signal processing applications.