Alternative algebra and Octonion

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Alternative algebra and Octonion

Alternative algebra vs. Octonion

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.

Similarities between Alternative algebra and Octonion

Alternative algebra and Octonion have 7 things in common (in Unionpedia): Associative property, Composition algebra, Involution (mathematics), Moufang loop, Octonion algebra, Sedenion, Subalgebra.

Associative property

In mathematics, the associative property is a property of some binary operations.

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Composition algebra

In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies for all and in.

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Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

Alternative algebra and Involution (mathematics) · Involution (mathematics) and Octonion · See more »

Moufang loop

In mathematics, a Moufang loop is a special kind of algebraic structure.

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Octonion algebra

In mathematics, an octonion algebra or Cayley algebra over a field F is an algebraic structure which is an 8-dimensional composition algebra over F. In other words, it is a unital non-associative algebra A over F with a non-degenerate quadratic form N (called the norm form) such that for all x and y in A. The most well-known example of an octonion algebra is the classical octonions, which are an octonion algebra over R, the field of real numbers.

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Sedenion

In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions.

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Subalgebra

In mathematics, a subalgebra is a subset of an algebra, closed under all its operations, and carrying the induced operations.

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The list above answers the following questions

What Alternative algebra and Octonion have in common
What are the similarities between Alternative algebra and Octonion

Alternative algebra and Octonion Comparison

Alternative algebra has 30 relations, while Octonion has 66. As they have in common 7, the Jaccard index is 7.29% = 7 / (30 + 66).

References

This article shows the relationship between Alternative algebra and Octonion. To access each article from which the information was extracted, please visit:

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