Part II — Eigenstructure, the Spectral Theorem, the DFT, and the SVD

Booklet: Abridged Math Foundations for Signals and Systems, Lessons 9–15 (PDF).

Complex vector spaces and complex exponentials; eigenvalues, eigenvectors, and diagonalization; self-adjoint operators and the spectral theorem; unitary matrices and the discrete Fourier transform; the singular value decomposition; determinants and trace.

24 exercises across Lessons 9–14 — 12 [Hand], 12 [Proof]. Lesson 15 is Capstone II (a project, no exercise block).

Exercises

Worked sets are linked below as they are completed.

• Lesson 9 — Complex Vectors and Complex Exponentials — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 10 — Eigenvalues, Eigenvectors, and Diagonalization — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 11 — Self-Adjoint Operators and the Spectral Theorem — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 12 — Unitary Matrices and the Discrete Fourier Transform — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 13 — The Singular Value Decomposition — 4 exercises (2 [Hand], 2 [Proof]) — ✓ done
• Lesson 14 — Determinants and Trace — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 15 — Capstone II: The DFT in NumPy — project