Any image is a matrix of numbers — here, ink densities. The SVD writes that matrix as a stack of simple rank-one plates, σ₁u₁v₁ᵀ + σ₂u₂v₂ᵀ + …, each weighted by a singular value σ.
The singular values fall off fast: the first few plates carry almost all the "ink energy", so a rank-k sum with small k already looks like the sitter. That is exactly how low-rank image compression works.
Switch to Scatter and the same instrument turns on a cloud of points. The SVD of the centered data is Principal Component Analysis — its singular vectors are the directions of greatest variance, the cloud's own natural axes.
So compression and PCA are one idea seen twice: keep the big singular values, drop the small ones.
The assay balance slipped mid-measurement. The lesson continues without it — everything you have already done is safe.