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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

Vector Dot Product Calculator

Compute the dot product of two 3D vectors as v1·v2 = v1x·v2x + v1y·v2y + v1z·v2z. Use it to measure projection, test orthogonality, or compute angles via the cosine formula.

Vector 1 - X component

Vector 1 - Y component

Vector 1 - Z component

Vector 2 - X component

V2 Y

V2 Z

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Key differences

	Gram-Schmidt Orthogonalization	Vector Dot Product Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	5	6
Result	Orthogonalization Result	Dot Product
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.	Compute the dot product of two 3D vectors as v1·v2 = v1x·v2x + v1y·v2y + v1z·v2z. Use it to measure projection, test orthogonality, or compute angles via the cosine formula.