Quaternions

Abstract

Abstract on quaternions and some applications by Riad Saad:
Number systems allow operations of addition, multiplication and division that come with certain properties, such as commutativity, distributivity, etc. We discuss quaternions as a number system and related representations. Then we present an extension of this system to even larger number system called octonions. The quaternions are members of a non-commutative division algebra first invented by William Rowan Hamilton. The quaternion number system can be considered as an extension of the complex number system. Hamilton defined a quaternion as the quotient of two direct lines in a three-dimensional space. Quaternions have various applications in geometry and physics representing three-dimensional rotations. They can be used alongside other methods of rotation, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application. Octonions are a kind of hypercomplex number system and have applications in string theory and quantum logic.

Details

Session 2

3:00pm – 4:30pm

Grand Salon