MATH-13 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Linear Algebra II: Eigenvalues and Decompositions
Playlist title reserved in the plan; no YouTube playlist or upload has been created yet.
Sign in to save this learning pathPractical outcome: Find a least-squares line for measured data.
Explain column space using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Explain orthogonal complements using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Explain orthogonal projections using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Explain gram-schmidt using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Use the first concepts from this section. Find a least-squares line for measured data. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain qr decomposition using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Explain least squares using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Explain normal equations using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Explain condition numbers using a visual and one worked real-world example. Context: Find a least-squares line for measured data. End with a prediction or check-for-understanding.
Find a least-squares line for measured data. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Column space, Orthogonal complements, Orthogonal projections and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Analyse repeated population transitions without claiming exact forecasts.
Explain determinants geometrically using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Explain cofactor expansion using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Explain eigenvalues using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Explain eigenvectors using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Use the first concepts from this section. Analyse repeated population transitions without claiming exact forecasts. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain characteristic polynomial using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Explain diagonalisation using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Explain symmetric matrices using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Explain spectral theorem using a visual and one worked real-world example. Context: Analyse repeated population transitions without claiming exact forecasts. End with a prediction or check-for-understanding.
Analyse repeated population transitions without claiming exact forecasts. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Determinants geometrically, Cofactor expansion, Eigenvalues and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare low-rank image approximations by reconstruction error.
Explain quadratic forms using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Explain positive definiteness using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Explain singular values using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Explain singular value decomposition using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare low-rank image approximations by reconstruction error. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain low-rank approximation using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Explain pseudoinverse using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Explain principal component geometry using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Explain jordan blocks using a visual and one worked real-world example. Context: Compare low-rank image approximations by reconstruction error. End with a prediction or check-for-understanding.
Compare low-rank image approximations by reconstruction error. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Quadratic forms, Positive definiteness, Singular values and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Compare low-rank image approximations by reconstruction error. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Linear Algebra II: Eigenvalues and Decompositions, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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