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Trigintaduonion
In abstract algebra, the trigintaduonions, also known as the , , form a commutative property, noncommutative and associative property, nonassociative algebra over a field, algebra over the real numbers. Names The word ''trigintaduonion'' is derived from Latin ' 'thirty' + ' 'two' + the suffix -''nion'', which is used for hypercomplex number systems. Other names include , , , and . Definition Every trigintaduonion is a linear combination of the unit trigintaduonions e_0, e_1, e_2, e_3, ..., e_, which form a Basis (linear algebra), basis of the vector space of trigintaduonions. Every trigintaduonion can be represented in the form :x = x_0 e_0 + x_1 e_1 + x_2 e_2 + \cdots + x_ e_ + x_ e_ with real coefficients . The trigintaduonions can be obtained by applying the Cayley–Dickson construction to the sedenions. Applying the Cayley–Dickson construction to the trigintaduonions yields a 64-dimensional algebra called the ''64-ions'', ''64-nions'', ''sexagintaquatronions'', or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley–Dickson Construction
In mathematics, the Cayley–Dickson construction, sometimes also known as the Cayley–Dickson process or the Cayley–Dickson procedure produces a sequence of algebra over a field, algebras over the field (mathematics), field of real numbers, each with twice the dimension of a vector space, dimension of the previous one. It is named after Arthur Cayley and Leonard Eugene Dickson. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied in mathematical physics. The Cayley–Dickson construction defines a new algebra as a Cartesian product of an algebra with itself, with multiplication defined in a specific way (different from the componentwise operation, componentwise multiplication) and an involution (mathematics), involution known as ''conjugation''. The product of an element and its complex conjugate, conjugate (or sometimes the square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
