PCA via SVD: centred X = UΣVᵀ, Eckart-Young best rank-k in Frobenius

Layer 2 — Chemistryin the chemometrics subtree

Principal-components analysis via the singular-value decomposition (Pearson 1901, Hotelling 1933; SVD foundations Eckart-Young 1936, Mirsky 1960). Take X ∈ ℝ^{n×p} with n observations (spectra, samples) × p features (wavelengths, m/z…

Related concepts

Singular value decomposition (SVD)
Orthogonality
Chemometrics (PCA, PLS, MCR)
SVD σ₁ of [[3],[4]] = 5 (Pythagorean-Frobenius witness)

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