latest-nb-n1

What's new

• Gram-Schmidt Core Logic Implementation for vector orthogonalization: Implemented the iterative projection and subtraction logic to convert linearly independent vectors into a strict orthonormal basis (Q)
• Computational Validation: Built-in verification step ensuring strict orthogonality using np.allclose(Q.T @ Q, np.eye)

# Verification: Q.T @ Q ≈ I
A = np.array([[1, 0, 0], [2, 0, 3], [4, 5, 6]]).T
assert np.allclose(gram_schmidt(A).T @ gram_schmidt(A), np.eye(3))  # ✓

Demo

🧪 Try it on Molab: Interactive Notebook
🤗 Try it on Hugging Face Spaces: Live Sandbox

A Visual Preview:

Further Updates

Up next on the roadmap:

1. GS Orthogonalization
2. QR Decomposition
3. Householder reflection & Bidiagonalization