Cartan Matrix Calculator
Generate accurate Cartan matrices for classical Lie algebras with proper labels and visual structure.
📘 User Guide (Click to Open)
What is a Cartan Matrix?
A Cartan matrix is a square integer matrix that encodes the angles and lengths between simple roots of a Lie algebra.
Matrix Properties
- Diagonal entries are always 2
- Off-diagonal entries are ≤ 0
- Aij = 0 ⇔ roots are orthogonal
- Encodes Dynkin diagram structure
Supported Types
- Aₙ – Linear chain
- Bₙ – One short root at end
- Cₙ – One long root at end
- Dₙ – Forked structure
How to Use
- Select Lie algebra type
- Enter rank (n)
- Click Generate
Example
For A₃:
[ 2 -1 0 ] [ -1 2 -1 ] [ 0 -1 2 ]