MML-05-04: Low-Rank Matrix Approximation & The Eckart-Young-Mirsky Theorem – Practice Quiz

35 worked single-select and multiselect questions. Tier 2–4. Prerequisites: QS 5.3. Learning goals: Formulate rank-constrained approximation and identify its norm; Compute spectral and Frobenius residuals from singular-value tails; Choose rank from error or energy budgets; Reconstruct low-rank matrices and compare candidate approximations; Distinguish optimality, uniqueness and repeated singular values; Derive optimality using null spaces and orthogonal dyads; Diagnose compression, denoising and semantic-retrieval limitations. Column gradients and output-by-input Jacobians are used where relevant. Detailed solutions explain every choice. References: Source 1, Source 2.