This workbench was generated by Claude (Anthropic) for the Linear Algebra 101 course materials. The decomposition is real. Your browser runs a one-sided Jacobi SVD on the actual pixel matrix and reconstructs A_k = Σ_i≤k σ_iu_iv_i^T from the computed factors. Nothing here is a blur, a downsample or a low-pass filter standing in for a truncation. The error you see printed is ‖A − A_k‖_F measured off the pixels, and it is shown beside the Eckart–Young closed form so you can watch the theorem hold.

One thing is cited rather than computed: the Eckart–Young theorem itself — that no rank-k matrix is closer to A than the truncated SVD. A web page cannot prove a theorem. What it can do is check the prediction at every k, which it does, and scripts/_svd_check.mjs goes further by sampling random rank-k perturbations and asserting none of them beats it.

C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrika, vol. 1, no. 3, pp. 211–218, 1936. Extended to every unitarily invariant norm by L. Mirsky, Quart. J. Math., vol. 11, pp. 50–59, 1960. One-sided Jacobi: J. Demmel and K. Veselić, SIAM J. Matrix Anal. Appl., vol. 13, no. 4, pp. 1204–1245, 1992.

The five test images are hand-designed teaching objects, not photographs and not a dataset — they are marked illustrative in the picker. Their pixels are computed from the stated recipe with a seeded generator, so the same settings always draw the same picture. One of them is rank 5 by construction: it must reconstruct exactly at k = 5, and it does. That is the sharpest checkable fact on the page.