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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.

Linear Algebra

Angle Between Vectors Calculator

Compute the angle in degrees between two 2D vectors using cos θ = (v1·v2)/(|v1|·|v2|) and the arccosine function. The result lies in [0°, 180°] regardless of vector orientation.

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 Process Calculator	Angle Between Vectors Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	5	4
Result	First Orthogonal Vector Magnitude	Angle Between Vectors (degrees)
What it does	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.	Compute the angle in degrees between two 2D vectors using cos θ = (v1·v2)/(\|v1\|·\|v2\|) and the arccosine function. The result lies in [0°, 180°] regardless of vector orientation.