Speakers:

• Professor J. K. Verma (IIT, Bombay, Mumbai)

Abstract:
We shall explain how rotations and reflections can be represented by orthogonal matrices. We shall prove Euler's Theorem which characterises rotations in terms of orthogonal matrices with determinant 1. We shall also prove a classical theorem of Cartan-Dieudonne which asserts that any  orthogonal matrix is a product of matrices of reflections in hyperplanes. If time permits, we shall find all finite subgroups of rotations of the plane.

Pre-requisites:
Eigenvalues of linear transformations

All are cordially invited to attend.