PCA 2×2 trace: λ₁+λ₂ = a+c = tr(C); λ₁·λ₂ = a·c−b² = det(C)

Layer 2 — Chemistryin the chemometrics subtree

Sympy-exact witness of the 2×2 PCA trace/determinant anchor — the smallest analytically-solvable case of Σλᵢ = tr(C) that still exhibits the full eigenvalue/trace/determinant correspondence. Setup: C = sp.Matrix([[a, b], [b, c]]) as a…

Related concepts

PCA trace framework: Σᵢ λᵢ = tr(C) (sum of eigenvalues equals total variance)
χ²(k=1) anchor: mean=1, variance=2

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