# Linear Algebra 2

Cursus

## Omschrijving

Linear algebra 2 is a sequel to 2MBA20 (Linear Algebra 1) and adresses linear maps between vector spaces, i.e., maps that are `compatible' with the linear structures of vector spaces. As (geometric) examples for linear maps, we have projections, reflections and rotations. The derivative of a function of two (or more) variables can also be viewed as a linear map, and linear maps are crucial in the study of quantum mechanics. There are many more applications since linear maps occur in many branches of mathematics and the sciences. In this course, we will discuss how linear maps can be described and dealt with by representing them via matrix representations. We also address how the nature of a linear map can be determined by simply looking at a given matrix representation. (For instance, how do you recognize that such a matrix represents a reflection?) This will involve switching between different bases (i.e., basis transformations) and an important technique to find characteristic properties (called eigenvalues and eigenvectors). We will use these techniques to proceed by studying interesting special classes of linear maps like orthogonal maps (linear maps that `preserve' shapes, like reflections and rotations) and symmetric maps (which can be used to analyse quadratic curves and surfaces like ellipses and hyperboloids).The techniques covered in this course also enable us to decompose matrices into products of `simpler' matrices in order to simplify certain mathematical tasks. E.g., such decompositions can be used to simplify the process of solving systems of linear equations like, e.g., certain types of linear differential equations.
Cursusperiode 1/09/23 → … Introductie Cursus