Jacobi Symmetric Plane Diagonalization

Rotate a symmetric matrix on both sides to eliminate coupling while preserving its spectrum.

Experiment with the Controls

You can interact with the diagonalization model at https://riano.app/module/jacobi-symmetric-plane-diagonalization.

1. Set First diagonal to 2, Second diagonal to 2, and Off diagonal to 1.
2. Observe that the rotation radians become exactly π/4 (~0.785398) because the diagonals are equal, meaning the matrix needs a 45-degree rotation to decouple.
3. Notice how the Off-diagonal energy after instantly becomes 0.
4. Set the Off diagonal to 0. The angle becomes 0, and the initial matrix is already diagonal.