hypercomplex number

Early in the 20th century, hypercomplex number systems were examined.

These can be interpreted as the bases of a hypercomplex number system.

A technical approach to hypercomplex numbers directs attention first to those of dimension two.

Kirkman's second research paper paper, in 1848, concerned hypercomplex numbers.

He is also known for contributions to space geometry, hypercomplex numbers, and criticism of early physical chemistry.

A matrix may be considered a hypercomplex number.

His interest concentrated on so-called higher complex numbers (nowadays called hypercomplex numbers).

Noncommutative ring theory began with attempts to extend the complex numbers to various hypercomplex number systems.

See hypercomplex numbers for other low dimensional examples.

Eduard Study had written an article on hypercomplex numbers for Klein's encyclopedia in 1898.

For example, the hypercomplex numbers of the nineteenth century had kinematic and physical motivations but challenged comprehension.

The concept of a hypercomplex number covered them all, and called for a science to explain and classify them.

The selection of rules of computation, which cannot be avoided in hypercomplex numbers, naturally allows some choice.

The quaternions were soon followed by several other hypercomplex number systems, which were the early examples of algebras over a field.

Most significantly, they identified the nilpotent and the idempotent elements as useful hypercomplex numbers for classifications.

First, matrices contributed new hypercomplex numbers like 2 x 2 real matrices.

As Hawkins (1972) explains, the hypercomplex numbers are stepping stones to learning about Lie groups and group representation theory.

There was even a professional research association, the Quaternion Society, devoted to the study of quaternions and other hypercomplex number systems.

It is thought that this will be achieved by combining of the invariants on each line into a single complex number (or hypercomplex number).

As for mathematics, the hyperbolic quaternion is another hypercomplex number, as such structures were called at the time.

As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems.

Eventually mathematics was concerned completely with abstract polynomials, complex numbers, hypercomplex numbers and other concepts.

Note however, that non-associative systems like octonions and hyperbolic quaternions represent another type of hypercomplex number.

In 14 (p 386) Scheffers reviews both German and English authors on hypercomplex numbers.

At its peak it consisted of about 60 mathematicians spread throughout the academic world that were experimenting with quaternions and other hypercomplex number systems.