Concept# Quaternionic analysis

Summary

In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range. Such functions can be called functions of a quaternion variable just as functions of a real variable or a complex variable are called.
As with complex and real analysis, it is possible to study the concepts of analyticity, holomorphy, harmonicity and conformality in the context of quaternions. Unlike the complex numbers and like the reals, the four notions do not coincide.
Properties
The projections of a quaternion onto its scalar part or onto its vector part, as well as the modulus and versor functions, are examples that are basic to understanding quaternion structure.
An important example of a function of a quaternion variable is
:f_1(q) = u q u^{-1}
which rotates the vector part of q by twice the angle represented by u.
The quaternion multiplicative inverse f_2(q) = q^{-1} is another fundamental function, but as with other number system

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

No results

Related people

Loading

Related units

No results

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people

Related concepts

No results

No results

Related courses

Related lectures

No results

No results