Six-step personalised learning roadmap

*(Abridged — Steps 1, 2 and 6 shown.)* **Step 1 — Skill tree** ``` Foundations (must come first) ├─ Vectors: notation, addition, scaling, dot product [low] ├─ Matrices as data vs. matrices as transformations [low] └─ Matrix multiplication, transpose, inverse [medium] Core ├─ Linear independence, span, basis, rank (needs: vectors, matmul) [medium] ├─ Orthogonality and projection (needs: dot product) [medium] └─ Solving Ax = b; least squares (needs: rank, projection) [medium] Target ├─ Eigenvalues and eigenvectors (needs: all of Core) [high] ├─ Covariance matrices (needs: projection) [high] └─ PCA = eigendecomposition of covariance (needs: both above) [high] ``` The foundational insight everything else rests on: a matrix is a function that moves vectors around. Every later topic is a question about what that function does. **Step 2 — Roadmap (10 weeks, ~6h/week)** | Weeks | Focus | Milestone | |---|---|---| | 1-2 | Vectors, matrices as transformations | Predict by hand what a 2x2 matrix does to the unit square | | 3-4 | Matmul, inverse, rank | Explain in one paragraph why a singular matrix has no inverse | | 5-6 | Independence, basis, projection | Project a vector onto a subspace in NumPy, no library solver | | 7-8 | Least squares, eigenvectors | Find eigenvectors of a 2x2 by hand and verify with NumPy | | 9-10 | Covariance, PCA | **Goal:** PCA from scratch on a real dataset | **Step 6 — Weekly shape (6 hours)** - Mon 45 min — new concept, video or text - Tue 45 min — code the concept in NumPy without library shortcuts - Thu 60 min — problem set on this week's topic - Sat 90 min — project work toward the PCA goal - Sun 30 min — spaced review: this week + week-minus-2 + week-minus-4 - Sun 30 min — write one paragraph explaining the week's concept from memory Weeks 4 and 8 replace new material with a checkpoint: rebuild the previous four weeks' code from a blank file. Whatever you cannot reconstruct goes back into the review rotation.