## SE425 : Topics in Applied Mathematics (Matrix groups)

Matrix groups are one of the most important mathematical objects used in pure mathematics. It is also used in applied mathematics (optimization), physics (Gauge theory), computer science (computational geometry), chemistry (molecular symmetries), mechanics (rigid motions), and so on.

- Real and complex matrix groups, Metric on matrix groups, Important examples of matrix groups
- Normed vector spaces, Action of matrix groups on vectors spaces, Continuous group actions
- Exponential and logarithm:
- Lie groups and Lie algebras
- SO(3) and SU(2)

- Clifford algebras and Spinor groups
- Lorentz groups'
- Semi-simple Lie groups and Root systems