Symmetric matrix eigenvalues

Worked example

a: 2	1
1	2

→ λ = 1; 3

Method and scope

Real symmetric matrices up to 6×6 only. Jacobi rotations diagonalize a scaled copy, with a limit of 100n² iterations. Each table row is a normalized eigenvector corresponding to λ. Repeated eigenvalues have no unique eigenvector basis. Nonsymmetric inputs are rejected.

Av ≈ λv; ‖v‖₂ = 1

Sources

• LAPACK — Error analysis
• Cornell — Jacobi iteration