# 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.