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New posts in octonions
Can octonions be used to rotate 7-dimensional vectors?
vectors
rotations
octonions
Octonionic formula for the ternary eight-dimensional cross product
cross-product
clifford-algebras
spin-geometry
octonions
Why do division algebras always have a number of dimensions which is a power of $2$?
binary
quaternions
division-algebras
octonions
sedenions
Can octonions be represented by infinite matrices?
abstract-algebra
matrices
representation-theory
octonions
nonassociative-algebras
The sixth number system
quaternions
number-systems
clifford-algebras
octonions
If there are any 3nion, 5nion, 7nion, 9nion, 10nion, etc.
complex-numbers
quaternions
octonions
Why is 8 so special?
number-systems
octonions
Is the seven-dimensional cross product unique?
lie-groups
cross-product
orthogonal-matrices
octonions
exceptional-isomorphisms
Why are properties lost in the Cayley–Dickson construction?
abstract-algebra
quaternions
octonions
sedenions
hypercomplex-numbers
What are some real-world uses of Octonions?
abstract-algebra
octonions
division-algebras
What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?
abstract-algebra
complex-numbers
quaternions
octonions
sedenions
What do we lose passing from the reals to the complex numbers?
complex-numbers
quaternions
division-algebras
octonions
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