Eig3x3.Eigendecomp — the pipeline driver

eigendecomp is the package's primary entry point. It owns all steps of the eigendecomposition pipeline:

• zero fast path,
• max-abs preconditioning (Eberly's overflow guard [Ebe14]),
• ordered eigenvalues on the scaled matrix (Habera–Zilian [HZ25]),
• isolated-eigenvalue-first eigenvector assembly (Eberly [Ebe14]),
• and eigenvalue rescaling.

def Eig3x3.eigendecomp (A : SymmMat3) : Decomposition

Full eigendecomposition of a real symmetric 3×3 matrix: A = QΛQᵀ = Σᵢ λᵢ cᵢcᵢᵀ with l₀ ≤ l₁ ≤ l₂ and Q right-handed orthonormal.

Pipeline: zero fast path → max-abs preconditioning (Eberly [Ebe14]) → ordered eigenvalues on the scaled matrix (Habera–Zilian [HZ25]) → eigenvector assembly consuming those eigenvalues (Eberly [Ebe14]) → eigenvalue rescaling.

Equations

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