Home > Sedenion

Like octonions, multiplication of sedenions is neither commutative nor associative. But in contrast to the octonions, the sedenions do not even have the property of being alternative. They do, however, have the property of being power-associative.

The sedenions have a multiplicative identity element 1 and multiplicative inverses, but they are not a division algebra. This is because they have zero divisors.

Every sedenion is a real linear combination of the unit sedenions 1, e₁, e₂, e₃, e₄, e₅, e₆, e₇, e₈, e₉, e₁₀, e₁₁, e₁₂, e₁₃, e₁₄ and e₁₅, which form a basis of the vector space of sedenions. The multiplication tableIn mathematics, a multiplication table is used to define a multiplication operation for an algebraic system. In basic arithmetic A multiplication table (as used to teach schoolchildren multiplication) is a grid where rows and columns are headed by the num of these unit sedenions looks as follows.