| 1 | Teaching the concept of inner product space |
| 2 | Ability to introduce norms and their applications |
| 3 | Teaching orthogonality and the Gram-Schmidt method |
| 4 | Ability to show linear transformations and their properties |
| 5 | Ability to explain eigenvalues and eigenvectors |
| 6 | Introducing the concepts of similar matrices, diagonalization and triangulation |