Linear algebra foundations
HE · 50 minutes · Work with matrices, spans and eigenvectors.
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Our learning goal
Work with matrices, spans and eigenvectors.
Your turn: Choose one thing you would like to understand by the end.
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Full teaching script
- Today: Linear algebra foundations. Our goal: Work with matrices, spans and eigenvectors.
- Take one idea at a time. Pause after each sentence; ask for repetition whenever you need it.
- A matrix is a linear map. Column space is where it can send things; the null space is what it crushes to zero; rank plus nullity equals the number of columns. Eigenvectors keep their direction under the map, scaled by their eigenvalue — the skeleton of the transformation.
- Together: choose one example from the explanation and show how it works. What do you notice?
- Your turn: Find the eigenvalues of [[2,1],[1,2]].
- Reflect: what made sense, and what would you like explained differently?
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