- Linearity, linear independence, vector spaces, norms
- Gaussian Elimination, LU and PTLU factorizations, Fundamental Subspaces
- Projections, Least Square and Minimum Norm Solutions
- State-Space Descriptions of Dynamical Systems, Canonical Forms
- Eigenvalues and Eigenvectors, Similarity Transformations
- Jordan Form
- State Transition Matrix
- Singular Value Decomposition
- Method of the Transfer Function, Transmission Zeros
- Controllability and Observability
- State-Feedback, State-Observers
- Model Based Compensators
- Linear Quadratic Regulators
- Linear Quadratic Gaussian and Loop Transfer Recovery