A small interactive 2D/3D visualization I built to improve my intuition for basis vectors and the reciprocal (dual) basis. You can adjust a basis with sliders and see how the reciprocal basis, dot products, and related quantities update in real time.
If you’re teaching or learning linear algebra, feel free to use this as a classroom demo or a quick visual aid.
- GitHub Pages: (https://ayman-alashkar.github.io/reciprocal_basis/)
- Non-orthonormal bases and how the reciprocal basis changes
- Dot products / Gram matrix intuition (and why the reciprocal basis is “dual” to the basis)
- 2D mode for simpler geometry + 3D mode for the full picture