Competencies, Evidence, and Remediation
Attempt the checkpoint independently after practice and labs. Use the separate key only afterward. Keep first attempts, proofs, counterexamples, code failures and changed-input results.
| Gate | Required independent evidence | Repair route |
|---|---|---|
| C1 Systems | Exact solve or inconsistency witness; complete solution set | Lessons 1–3, P1–P2, Lab 1 |
| C2 Spaces | Correct bases, dimensions, ambient spaces and closure hypotheses | Lessons 4–6, P3–P5 |
| C3 Coordinates | Basis conversion derived with correct order and shape | Lessons 6–7, P6–P7 |
| C4 Approximation | Orthogonal-residual optimality; fit versus coefficient uniqueness | Lessons 8–9, P8–P9, Lab 2 |
| C5 Determinants | Volume/orientation with a separate conditioning argument | Lesson 10, P10 |
| C6 Spectra | Field, eigenbasis, starting-component and convergence limitations | Lessons 11–12, P11–P12, Lab 3 |
| C7 Positive structure | Valid PD proof, factor verification and PSD counterexample | Lesson 13, P13/P15 |
| C8 SVD | Shapes, two tail errors, nonuniqueness and cutoff interpretation | Lesson 14, P14–P17, Lab 4 |
| C9 Error analysis | Named norms; residual, backward error and conditioning | Lesson 15, P16–P17, Lab 4 |
| C10 Method judgment | Solver assumptions and honest changed-objective decisions | P18–P20, numerical experiments, project |
Score each gate: 0 missing/incorrect; 1 partly correct with a material gap or help; 2 correct independent derivation and interpretation; 3 also handles a changed assumption and explains a counterexample. Completion requires at least two in every gate, all four lab evidence packets and the project. Do not average away a failed gate. Passing code alone cannot establish a proof gate.
Critical errors include using reduced columns as an original column-space basis, inverting a rectangular basis, treating a small residual as proof of accuracy, claiming every power iteration finds a dominant mode, and silently truncating or regularizing a model. Repair the relevant lesson and solve a fresh instance.
Allow 10–16 hours for checkpoint, oral explanation and remediation, not a single speed exam. After 7–14 days recheck one structural gate and one numerical gate on unseen inputs. Record assistance and solution exposure. Independent reviewers and learner pilots remain pending; this rubric is an authored standard.