The Outline of the Course
The following are two main mathematical objects that we will study in this course:
They are studied in an important branch of mathematics called "linear algebra". Matrices belong to the computation side of linear algebra, whereas vectors belong to the geometric side of it. In this course, we will study both and their relationships in detail.
As you will see, we will mainly use vectors in or as examples because they can be more easily illustrated in GeoGebra applets. However, the same theory can readily be extended to higher dimensional spaces. Therefore, most of the theorems that you will see in this course are also valid in general n-dimensional spaces.
- Matrices
- Vectors
| Vectors | Matrices |
| Vectors / points in | 2x1 column matrices |
| Vectors / points in | 3x1 column matrices |
| Vector addition | Matrix addition |
| Scaling a vector | Scalar multiplication |
| Linear Transformations from to | 2x2 matrices |
| Linear Transformations from to | 3x3 matrices |
Outline
The following is the outline of this course:
- Definition of a vector and its matrix representation
- Vector addition and scaling, linear combination, span
- Linear independence, basis, dimension
- Linear transformations
- Systems of linear equations
- Gaussian elimination
- Solving systems of linear equations
- Computing the inverse of a matrix
- Determinants
- General vector spaces
- Column space and null space
- Rank theorem
- Eigenvalues and eigenvectors
- Diagonalization
- Inner product and orthogonality
- Orthogonal projections and Gram-Schmidt process
- Least square method