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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

Matrix Trace and Properties Calculator

Compute the trace, Frobenius norm, spectral radius, and other key properties of a matrix in one place. Useful for checking matrix health, eigenvalue bounds, and verifying theoretical results in linear algebra.

Property to Calculate

Matrix Order

Diagonal Element (1,1)

Diagonal Element (2,2)

Diagonal Element (3,3)

Sum of Off-diagonal Elements

Fill in the required fields to see your result.

Key differences

	Gram-Schmidt Orthogonalization Calculator	Matrix Trace and Properties Calculator
Category	Linear Algebra	Linear Algebra
Inputs required	4	6
Result	Second Orthogonal Vector Magnitude (units)	Matrix Property Value
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.	Compute the trace, Frobenius norm, spectral radius, and other key properties of a matrix in one place. Useful for checking matrix health, eigenvalue bounds, and verifying theoretical results in linear algebra.