Examples of 'octonions' in a sentence
Meaning of "octonions"
octonions (noun): Octonions are a type of hypercomplex number system that extends the concept of complex numbers. They consist of 8 dimensions and have properties different from those of quaternions and complex numbers
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- plural of octonion
How to use "octonions" in a sentence
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octonions
The octonions are connected to a wide variety of exceptional objects.
The reason for this is that octonions are not associative.
The nonzero octonions form a nonassociative loop under multiplication.
There are several natural ways to choose an integral form of the octonions.
Complex octonions have been used to describe the generations of quarks and leptons.
Found in the octonions.
This implies that the octonions form a nonassociative normed division algebra.
All the steps to create further algebras are the same from octonions on.
The simplest is just to take the octonions whose coordinates are integers.
The latter two derived it while working on an extension of quaternions called octonions.
The octonions are a special type of loop known as a Moufang loop.
Sphere Almost complex structure coming from the set of pure unit octonions.
For example, octonions are not associative.
This gives a nonassociative algebra over the integers called the Gravesian octonions.
Addition of octonions is also associative, but multiplication of octonions is non-associative.
See also
Quaternions and Octonions.
The quaternions, octonions and sedenions are generated by the Cayley-Dickson construction.
Functions for complex numbers, quaternions and octonions.
A more systematic way of defining the octonions is via the Cayley-Dickson construction.
The sporadic SICs in dimension 8 are related to the integral octonions.
Octonions have applications in fields such as string theory, special relativity and quantum logic.
Applying the Cayley-Dickson construction to the octonions produces the sedenions.
The octonions are a normed division algebra over the real numbers, the largest such algebra.
Lacking the desirable property of associativity, the octonions receive far less attention than the quaternions.
Octonions are related to exceptional structures in mathematics, among them the exceptional Lie groups.
The E8 lattice can be realized as the integral octonions up to a scale factor.
The imaginary octonions form a Malcev algebra with the Malcev product xy - yx.
Supported fields, complex, quaternions and octonions.
A more systematic way of defining the octonions is via the Cayley - Dickson construction.
This sum-of-squares identity is characteristic of composition algebra, a feature of complex numbers, quaternions, and octonions.
An automorphism, A, of the octonions is an invertible linear transformation of O which satisfies.
The octonions can be thought of as octets ( or 8-tuples ) of real numbers.
In particular, octonions are non-associative.
The octonions are 8-dimensional.
Because of their non-associativity, octonions do not have matrix representations, unlike quaternions.
