A Tour of the Matrix GroupsIn linear algebra, we learn about
matrices and how they can be used to represent linear transformations of
n-dimensional real space. Later on, in abstract algebra, we learn about
groups. In this talk, we'll tie the two together with an exploration of
matrix groups. Our focus will be to understand visually what the different
matrix groups represent, and how they are related to each other. At the
end of the talk, we'll learn how the isometries of n-dimensional space can be
represented as a semi-direct product of a matrix group with a group of
translations.
Despite all the groups sprinkled through the
talk, it will be accessible to anyone who has had or is currently taking linear
algebra. There won’t be any Calculus and there will be many
pictures and explanations so all are welcome!