Description

Linear algebra 2 is a sequel to 2WF20 Linear Algebra 1 and adresses linear maps between vector spaces, i.e., maps that `respect' linearity. Projections, reflections and rotations are (geometric) examples of such linear maps, but there are many more types. Linear maps occur in many branches of mathematics and the sciences. For instance, they are closely related to the derivative of a function of two or more variables, but are also crucial in the study of quantum mechanics. In Linear Algebra 2 we discuss the role of matrices in describing and handling linear maps. We also address the question of determining the nature of a linear map given a matrix representation of it (for instance, how do you recognize a reflection from such a matrix?). This involves basis transformations and the important technique of finding eigenvalues and eigenvectors of linear maps. Using these techniques special classes of linear maps are studied: orthogonal maps (linear maps that `preserve' shapes, like reflections and rotations) and symmetric maps that can be used to analyse quadratic curves and surfaces like ellipses and hyperboloids. Our techniques also enable us to decompose matrices as products of `easier' matrices in order to simplify, for instance, the solution process of a system of linear equations. Another important application of our eigenvalue-eigenvector techniques is concerned with solving systems of linear differential equations.
Course period1/09/12 → …
Course levelIntroductory
Course formatCourse