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Geometric algebra and Octonion

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

Difference between Geometric algebra and Octonion

Geometric algebra vs. Octonion

The geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements called multivectors, which is a superset of both the scalars F and the vector space V. Mathematically, a geometric algebra may be defined as the Clifford algebra of a vector space with a quadratic form. 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 Geometric algebra and Octonion

Geometric algebra and Octonion have 13 things in common (in Unionpedia): Associative property, Automorphism, Bivector, Complex number, Cross product, Distributive property, Gamma matrices, Hodge star operator, Kronecker delta, Quaternion, Real number, William Rowan Hamilton, Zero divisor.

Associative property

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

Associative property and Geometric algebra · Associative property and Octonion · See more »

Automorphism

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

Automorphism and Geometric algebra · Automorphism and Octonion · See more »

Bivector

In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.

Bivector and Geometric algebra · Bivector and Octonion · See more »

Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

Complex number and Geometric algebra · Complex number and Octonion · See more »

Cross product

In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.

Cross product and Geometric algebra · Cross product and Octonion · See more »

Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

Distributive property and Geometric algebra · Distributive property and Octonion · See more »

Gamma matrices

In mathematical physics, the gamma matrices, \, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cℓ1,3(R).

Gamma matrices and Geometric algebra · Gamma matrices and Octonion · See more »

Hodge star operator

In mathematics, the Hodge isomorphism or Hodge star operator is an important linear map introduced in general by W. V. D. Hodge.

Geometric algebra and Hodge star operator · Hodge star operator and Octonion · See more »

Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

Geometric algebra and Kronecker delta · Kronecker delta and Octonion · See more »

Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers.

Geometric algebra and Quaternion · Octonion and Quaternion · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

Geometric algebra and Real number · Octonion and Real number · See more »

William Rowan Hamilton

Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.

Geometric algebra and William Rowan Hamilton · Octonion and William Rowan Hamilton · See more »

Zero divisor

In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.

Geometric algebra and Zero divisor · Octonion and Zero divisor · See more »

The list above answers the following questions

Geometric algebra and Octonion Comparison

Geometric algebra has 147 relations, while Octonion has 66. As they have in common 13, the Jaccard index is 6.10% = 13 / (147 + 66).

References

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

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