LESSON 0.3 · Theory · 120 min
The linear algebra models actually use
The linear algebra models actually use. Learn vector spaces, matrix multiplication, basis changes, eigenvalues, and SVD intuition and complete: Implement a NumPy linear layer and t
Learning objectives
- Explain what problem “The linear algebra models actually use” solves without hiding behind terminology.
- Trace the variables and causal links across vector spaces, matrix multiplication, basis changes.
- Complete “Implement a NumPy linear layer and trace every shape” and judge the result with evidence rather than intuition.
Core concepts
vector spaces
vector spaces is part of the lesson’s causal model. State its inputs, outputs, invariants, and failure mode; then verify it with a hand-check or a minimal experiment before moving to an optimized implementation.
matrix multiplication
matrix multiplication is part of the lesson’s causal model. State its inputs, outputs, invariants, and failure mode; then verify it with a hand-check or a minimal experiment.
basis changes
basis changes is part of the lesson’s causal model. State its inputs, outputs, invariants, and failure mode; then verify it with a hand-check or a minimal experiment.
eigenvalues
eigenvalues is part of the lesson’s causal model. State its inputs, outputs, invariants, and failure mode; then verify it with a hand-check or a minimal experiment.
and SVD intuition
and SVD intuition is part of the lesson’s causal model. State its inputs, outputs, invariants, and failure mode; then verify it with a hand-check or a minimal experiment.
Build and verify
Implement a NumPy linear layer and trace every shape
- Predict: write the expected output, trend, or failure before running code.
- Build: implement only the minimum components needed to answer the question.
- Verify: compare with a baseline or trusted implementation; save seeds, parameters, and raw outputs.
- Transfer: change one shape, dataset, scale, or workload condition and explain whether the conclusion still holds.