- mathematics, the
octonions are a
normed division algebra over the real numbers, a kind of
hypercomplex number system. The
octonions are
usually represented...
- {C} ,} the
quaternions H , {\displaystyle \mathbb {H} ,} and
lastly the
octonions O , {\displaystyle \mathbb {O} ,}
where the
dimensions of
these spaces...
-
Fixing a
basis (1, i, j, k, ℓ, ℓi, ℓj, ℓk) of unit
octonions, one can
define the
integral octonions as a
maximal order containing this basis. (One must...
- the
octonions. The
Cayley plane was
discovered in 1933 by Ruth Moufang, and is
named after Arthur Cayley for his 1845
paper describing the
octonions. In...
- and
quaternions are ****ociative.
Addition of
octonions is also ****ociative, but
multiplication of
octonions is non-****ociative. The
greatest common divisor...
-
example of an
octonion algebra is the
classical octonions,
which are an
octonion algebra over R, the
field of real numbers. The split-
octonions also form...
- of
octonions is even
stranger than that of quaternions;
besides being non-commutative, it is not ****ociative – that is, if p, q, and r are
octonions, it...
- mathematics, the split-
octonions are an 8-dimensional non****ociative
algebra over the real numbers.
Unlike the
standard octonions, they
contain non-zero...
- {CD}}(\mathbb {O} ,1)} . As such, the
octonions are
isomorphic to a
subalgebra of the sedenions.
Unlike the
octonions, the
sedenions are not an alternative...
- the
octonions (dimension 8). The
quaternions and
octonions are not commutative. Of
these algebras, all are ****ociative
except for the
octonions. Quadratic...
