After his habilitation, Hausdorff wrote another work on optics, on non-Euclidean geometry, and on hypercomplex number systems, as well as two papers on probability theory.
22.
This result was given in 1907 Joseph Wedderburn in his doctoral thesis, " On hypercomplex numbers ", which appeared in the Proceedings of the London Mathematical Society.
23.
In the early 20th century, matrices attained a central role in linear algebra . partially due to their use in classification of the hypercomplex number systems of the previous century.
24.
Modern terminology is " algebra " for " system of hypercomplex numbers ", and the algebras used in applications are often Banach algebras since Cauchy sequences can be taken to be convergent.
25.
Of course, you can construct other types of numbers by " starting " with stuff outside of the complex numbers in the first place-see quaternions for one example, and hypercomplex numbers for other examples.
26.
Wedderburn's best-known paper was his sole-authored " On hypercomplex numbers, " published in the 1907 Proceedings of the London Mathematical Society, and for which he was awarded the D . Sc . the following year.
27.
The " output ", also called the " value of the function ", could be anything : simple examples include a single real number, or a fields, such as complex numbers, quaternions, or even more exotic hypercomplex numbers.
28.
Returning to Scotland in 1905, Wedderburn worked for four years at the University of Edinburgh as an assistant to George Chrystal, who supervised his D . Sc, awarded in 1908 for a thesis titled " On Hypercomplex Numbers ".
29.
This article exhibits these examples of the use of hyperbolic motions : the extension of the metric d ( a, b ) = \ vert \ log ( b / a ) \ vert to the half-plane, and in the location of a quasi-sphere of a hypercomplex number system.
30.
Thus, for example, the studies of " hypercomplex numbers ", such as considered by the Quaternion Society, were put onto an axiomatic footing as branches of ring theory ( in this case, with the specific meaning of associative algebras over the field of complex numbers . ) In this context, the quotient ring concept is one of the most powerful unifiers.
