Automorphism and Octonion

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

Difference between Automorphism and Octonion

Automorphism vs. Octonion

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

Associative property

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

Associative property and Automorphism · Associative property 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.

Automorphism and Complex number · Complex number and Octonion · See more »

G2 (mathematics)

In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras \mathfrak_2, as well as some algebraic groups.

Automorphism and G2 (mathematics) · G2 (mathematics) and Octonion · See more »

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

Automorphism and Group (mathematics) · Group (mathematics) and Octonion · See more »

Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.

Automorphism and Inverse element · Inverse element and Octonion · See more »

Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

Automorphism and Isomorphism · Isomorphism and Octonion · See more »

Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

Automorphism and Linear map · Linear map and Octonion · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Automorphism and Mathematics · Mathematics and Octonion · See more »

Philosophical Magazine

The Philosophical Magazine is one of the oldest scientific journals published in English.

Automorphism and Philosophical Magazine · Octonion and Philosophical Magazine · See more »

Quaternion

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

Automorphism 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.

Automorphism 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.

Automorphism and William Rowan Hamilton · Octonion and William Rowan Hamilton · See more »