Quaternion Linear Algebra

Dylan Johnson

In this talk we will cover some basic properties of the quaternion division ring, quaternion vector spaces, matrices with quaternion entries, and present some open problems in the field. We first introduce the quaternions and present their automorphisms, involutions, and matrix representations. Finite dimensional quaternion vector spaces and quaternion matrices are introduced followed by the quaternion version of various linear algebra topics, including canonnical forms, invariant subspaces, eigenvectors & eigenvalues, determinant, and numerical range. This will be a very accessible talk, with only knowledge of undergraduate linear algebra needed to follow most of the presentation.

To participate in this event virtually via Zoom, go to https://uiowa.zoom.us/j/95316149275.