Part I — The Linear Algebra Core

Booklet: Abridged Math Foundations for Signals and Systems, Lessons 1–8 (PDF).

The linear algebra core: vectors and linear combinations; dot products, norms, and orthogonality; span, independence, basis, and dimension; matrices as linear maps; null space and rank; orthogonal projections and least squares; gradients.

29 exercises across Lessons 1–7 — 14 [Hand], 15 [Proof]. Lesson 8 is Capstone I (a project, no exercise block).

Exercises

Worked sets are linked below as they are completed.

• Lesson 1 — Vectors and Linear Combinations — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 2 — Dot Products, Norms, and Orthogonality — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 3 — Span, Linear Independence, Basis, Dimension — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 4 — Matrices and Linear Maps — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 5 — Null Space, Rank, and Solving \(Ax=b\) — 5 exercises (2 [Hand], 3 [Proof]) — ✓ done
• Lesson 6 — Orthogonal Projections and Least Squares — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 7 — Gradients for Machine Learning — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 8 — Capstone I: Linear Regression from Scratch — project