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## Lecture: Review of Matrix Manipulations (45 minutes)

Use the handout below to review basic matrix operations. A good review is to pose an example of each operation, using simple numbers, and ask students to write the result on their small whiteboards. Spend time reviewing those operations that are tricky.

- A pretest can be given on basic matrix manipulations to test students' prior knowledge of basic matrix manipulation. This will alert the students to the thing that they most need to know.
- Review of matrix addition, multiplication, commutator, transpose, Hermitian adjoint, determinants, inverses. For most students, only the commutator and Hermitian adjoint are new concepts.
- Each matrix manipulation introduced by posing an example, using simple numbers, and ask the studentds to write the result on their individual whiteboards. Then discuss the technique briefly with the whole class.
- After introducing the idea of the Hermitian adjoint, ask the students to determine (with their near neighbors) the properties a matrix must have for it to be Hermitian (equal to its own hermitian adjoint). Discuss with the whole class.
- Individual students know different ways of finding the determinant of a 3×3 matrix. It can be confusing introducing a new method. To save time and avoid confusion, we do not give a method in class, rather, we give them practice problems for homework and work with individual students who need help. Tell students how to look up a method if they ever need to find the determinant of matrices larger that 3×3.

Student handout: