Protocol
Linear Algebra Through Stable Solvers
Compress a small matrix or grayscale image using SVD. Choose a rank under a storage budget and distinguish approximation error from solver instability.
45–70 active hours60–90 min sessionsBeginner
Mastery contract
Core protocol · Standard 1.0 · Compress a small matrix or grayscale image using SVD. Choose a rank under a storage budget and distinguish approximation error from solver instability.
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Reasoning — not yet passed
Derive the projection and identify when the least-squares solution is unique, including a rank-deficient counterexample.
Reliable implementation — not yet passed
The implementation passes orthogonality/reconstruction checks at a stated tolerance on well-conditioned fixtures.
Reproducible experiment — not yet passed
Report sensitivity under a fixed perturbation and explain why a small residual does not guarantee accurate coefficients.
Defense and handoff — not yet passed
Defend a low-rank reconstruction of a small matrix using singular values, measured error and a rank-selection rationale.
All four criteria must pass. Activity completion does not satisfy them.
An independent reviewer reruns your work and varies something you did not rehearse: a fresh input, a different working directory, or a declared edge case.
Pilot decisions are provisional, not external credentials. For an appeal or sensitive artifact, contact your designated pilot operator with the submission ID. Export your assessment history.
What you will do
6 total
Derive an orthogonal projection and the normal equations on a 3-by-2 example; explain uniqueness using rank and null spaces.
Implement Gram–Schmidt and a projection solver without a regression library; compare with NumPy QR/SVD and verify orthogonality and residuals.
Construct 3 matrices with increasing column dependence; compare residual norm, coefficient sensitivity and SVD truncation error after a fixed perturbation.
Debug a transposed basis and a singular normal-equation solve; show why a pseudoinverse or QR is appropriate and explicit inversion is fragile.
Write a 500–900 word technical report linking the reasoning, code, measurements, and limitations; include the project decision below.
Assess all 4 mastery criteria against saved artifacts, request an independent review, and repeat each failed criterion on a fresh example.
Essentials
A reading session alone never satisfies a mastery criterion.
Store source references, assumptions, and artifact paths beside every result.
Keep an untouched check case that differs from the worked example.
Record all attempts, including failures and results that contradict your prediction.
Use the stated comparison conditions; document every deviation before drawing a conclusion.
Protocol guardrails
Do
- +State the expected result before running the comparison.
- +Keep one minimal reproducible failing case when debugging.
- +Record environment versions and the exact command used.
- +Compare explanations with saved intermediate values.
- +Ask a reviewer to challenge the weakest assumption.
Don't
- ×Do not copy a worked solution and present it as an independent implementation.
- ×Do not tune against held-out evaluation outcomes.
- ×Do not report only the best seed or discard inconvenient runs.
- ×Do not equate elapsed hours or a completed run with a passed assessment.
- ×Do not conceal reduced-scale experiments behind claims about the original full-scale result.
Protocol authorship
Written by NuthinButta as instructional design. The teaching sources are the official references linked in each milestone; the exercises, workload and pass thresholds are ours, not their authors'.