High Quality Content by WIKIPEDIA articles! In abstract algebra, sedenions form a 16-dimensional non-associative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions. The set of sedenions is denoted by mathbb{S}. The term "sedenion" is also used for other 16-dimensional algebraic structures, such as a tensor product of 2 copies of the quaternions, or the algebra of 4 by 4 matrices over the reals, or that studied by Smith (1995). Like (Cayley–Dickson) octonions, multiplication of Cayley–Dickson 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 power associativity. 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.

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