- mathematics, the
octonions are a
normed division algebra over the real numbers, a kind of
hypercomplex number system. The
octonions are
usually represented...
- mathematics, the split-
octonions are an 8-dimensional non****ociative
algebra over the real numbers.
Unlike the
standard octonions, they
contain non-zero...
- Cayley–****son algebras, for
example complex numbers, quaternions, and
octonions.
These examples are
useful composition algebras frequently applied in...
- In mathematics, an
octonion algebra or
Cayley algebra over a
field F is a
composition algebra over F that has
dimension 8 over F. In
other words, it is...
- The seven-dimensional
cross product has the same
relationship to the
octonions as the three-dimensional
product does to the quaternions. The seven-dimensional...
- real
octonions O. It is
possible to
define the
concept of an
integral octonion analogous to that of an
integral quaternion. The
integral octonions naturally...
- {C} ,} the
quaternions H , {\displaystyle \mathbb {H} ,} and
lastly the
octonions O , {\displaystyle \mathbb {O} ,}
where the
dimensions of
these spaces...
- The
Geometry of the
Octonions is a
mathematics book on the
octonions, a
system of
numbers generalizing the
complex numbers and quaternions, presenting...
- The
compact form of G2 can be
described as the
automorphism group of the
octonion algebra or, equivalently, as the
subgroup of SO(7) that
preserves any chosen...
-
sedenions are
obtained by
applying the Cayley–****son
construction to the
octonions,
which can be
mathematically expressed as S = C D ( O , 1 ) {\displaystyle...
