My notes for when I took this course in Fall 2024, taught by Babak Ayazifar and JP Tennant.

Course by Week

Week Topics
1 Vectors, Linear Combination, Parallelogram Law Complex Algebra
2 Vector Spaces, Norms, Dimension
3 Inner Product, Cauchy-Schwartz, Linear Dependence, Distance Midterm 1
4 Span, Orthogonality, Bases
5 Discrete Time Fourier Series and Complex Exponentials
6 Gram-Schmidt, Projection, Orthonormalization
7 Matrices, Outer Product, Matrix Multiplication
8 Fundamental Subspaces, Rank-Nullity Theorem, QR Factorization, Inverses Midterm 2
9 Determinants, Eigenvalues, Diagonalization, Change of Basis
10 Projection Matrices, Least Squares, Orthogonal Matrices, Symmetric Matrices, Spectral Theorem
11 Singular Value Decomposition, Moore-Penrose Pseudoinverse, Principal Component Analysis
PCA Lecture
12 System State, Superposition Principle, Scalar Differential and Scalar Difference Equations
13 Matrix Exponential, State Space Conversion, Vector Differential and Vector Difference Equations
15 Internal and External Stability, Feedback Control Midterm 3

Course by Content

Linear Algebra

Vectors

Vectors, Linear Combination, Parallelogram Law

Vector Spaces, Norms, Dimension

Inner Product, Cauchy-Schwartz, Linear Dependence, Distance

Span, Orthogonality, Bases

Gram-Schmidt, Projection, Orthonormalization

Matrices

Matrices, Outer Product, Matrix Multiplication

Fundamental Subspaces, Rank-Nullity Theorem, QR Factorization, Inverses

Determinants, Eigenvalues, Diagonalization, Change of Basis

Projection Matrices, Least Squares, Orthogonal Matrices, Symmetric Matrices, Spectral Theorem

Singular Value Decomposition, Moore-Penrose Pseudoinverse, Principal Component Analysis

PCA Lecture

Fourier Analysis

Complex Algebra

Discrete Time Fourier Series and Complex Exponentials

Differential Equations and Control

System State, Superposition Principle, Scalar Differential and Scalar Difference Equations

Matrix Exponential, State Space Conversion, Vector Differential and Vector Difference Equations

Internal and External Stability, Feedback Control

Appendix

The following is a collection of useful tips in no particular order.

  1. If $x(n)$ is real, then the following applies to its Fourier coefficients $X_k = X_{-k}^*$
  2. If a T-periodic signal is overestimated with a Fourier series of $kT$ terms, then there will be vacuous coefficients (redundant coefficients that are zero).