### Unit: Matrices and Vectors

#### Matrix Manipulations (45 minutes)

- Review of matrix manipulations (Lecture, 45 minutes)

#### Introduction to Bra-ket notation (15 minutes)

- Introduction to bra-ket notation (Lecture, ?? minutes) - Emphasize normalization and finding components. Add a good SWBQ or small group activity.

### Unit: Operators and Transformations in Linear Systems

#### Linear Transformations (1 1/2 hr)

- Linear Transformations Activity (Small Group Activity)

#### Tangible Metaphor for Complex Vectors (10 minutes)

- Visualizing Complex Two Component Vectors (Kinesthetic Activity)

#### Properties of Linear Vector Spaces (30 min)

- Properties of linear vector spaces (Optional Lecture, ?? minutes)

#### Inner Products and Norms

- Calculating Inner Products and Normalization of Vectors (Lecture, ?? minutes)

Write these lecture notes. Emphasize complex vectors.

#### Matrix Components (40 min)

- Finding Matrix Elements (Small Group Activity) Work in comments about Fourier series into wrap-up.

#### Rotation Matrices in 2 and 3 Dimensions (10 min)

- Rotation Matrices in 2 and 3 Dimensions (Lecture, ?? minutes).

### Unit: Eigenvalues and Eigenvectors

#### Eigenvalues & Eigenvectors (2 hr)

- Eigenvectors and Eigenvalues Activity (Small Group Activity)

#### Special Properties of Hermitian Matrices (40 min)

- Properties of Hermitian matrices (Lecture, ?? minutes)
- Diagonalization of matrices (Lecture, ?? minutes)
- Diagonalizing Matrices (Small Group Activity).

#### Commuting Matrices (10 min)

- Properties of commuting matrices (Lecture, ?? minutes)