Linear Algebra in the Euclidean Plane
That course gives you many important skills in linear algebra in dimension 2, the fundamental scope to be ready for linear algebra in any dimension.
The course will provide a comprehensive introduction to the highly beneficial subject of linear algebra. The initial stage involves a detailed exploration of linear algebra in the Euclidean plane. Upon completion of the course, you will have the capability to execute the subsequent mathematical operations.
- Solve systems of two linear equations with two variables.
- Utilise, graph, and manipulate vectors in the plane.
- Compute and apply dot products and norms of vectors in the Euclidean plane.
- Define and manipulate angles, along with their trigonometric functions.
- Determine and utilize polar coordinates of a nonzero vector.
- Work with and manipulate complex numbers, visualizing their vector representations.
- Perform calculations involving matrices of linear transformations.
- Identify bases in the plane and compute transition matrices for changing bases.
- Compute eigenvalues and eigenvectors of a matrix, utilising them for matrix diagonalisation.
- Lastly, diagonalise matrices in ℂ that have no real eigenvalues.
All of these concepts will be taught from a practical perspective, incorporating graphics and Python sessions and scripts.
Your Instructor
Fabienne holds the Agregation in Mathematics, the highest French diploma to teach mathematics in secondary schools. After a 26-year career as an R&D engineer in applied mathematics, she founded Mathedu (Mathematics Re-engineering) with her husband and collaborator Francois, to teach mathematics from a practical point of view, based on Python programming. She is both an expert in mathematics education and a passionate woman who will help you experience the joy of improving your mastery of mathematics.