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Both calculators run independently — change the inputs on either side to compare results.

Gram-Schmidt Orthogonalization Calculator

Convert two linearly independent 2D vectors into an orthonormal basis using the Gram-Schmidt process. Ideal for linear algebra students working on QR decomposition, subspace projections, or eigenvalue problems.

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.

Linear Algebra

Linear Transformation Matrix Calculator

Apply 2D linear transformations — rotation, scaling, reflection, and shearing — to any input vector. Ideal for computer graphics, robotics, and linear algebra coursework.

Transformation Type

Angle (degrees) (°)

X-axis Scale Factor

Input Vector X

Input Vector Y

Fill in the required fields to see your result.

Key differences

	Gram-Schmidt Orthogonalization Calculator	Linear Transformation Matrix Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	4	5
Result	Second Orthogonal Vector Magnitude (units)	Transformed X Component
What it does	Convert two linearly independent 2D vectors into an orthonormal basis using the Gram-Schmidt process. Ideal for linear algebra students working on QR decomposition, subspace projections, or eigenvalue problems.	Apply 2D linear transformations — rotation, scaling, reflection, and shearing — to any input vector. Ideal for computer graphics, robotics, and linear algebra coursework.