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N-sphere and Orthogonal group

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

Difference between N-sphere and Orthogonal group

N-sphere vs. Orthogonal group

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension. In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

Similarities between N-sphere and Orthogonal group

N-sphere and Orthogonal group have 16 things in common (in Unionpedia): Circle, Circle group, Connected space, Dimension, Euclidean space, Homotopy groups of spheres, Mathematics, Octonion, Orthogonal group, Real number, Real projective line, Riemann sphere, Simply connected space, Sphere, Symplectic group, 3-sphere.

Circle

A circle is a simple closed shape.

Circle and N-sphere · Circle and Orthogonal group · See more »

Circle group

In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.

Circle group and N-sphere · Circle group and Orthogonal group · See more »

Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.

Connected space and N-sphere · Connected space and Orthogonal group · See more »

Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

Dimension and N-sphere · Dimension and Orthogonal group · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

Euclidean space and N-sphere · Euclidean space and Orthogonal group · See more »

Homotopy groups of spheres

In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other.

Homotopy groups of spheres and N-sphere · Homotopy groups of spheres and Orthogonal group · See more »

Mathematics

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

Mathematics and N-sphere · Mathematics and Orthogonal group · See more »

Octonion

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.

N-sphere and Octonion · Octonion and Orthogonal group · See more »

Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

N-sphere and Orthogonal group · Orthogonal group and Orthogonal group · See more »

Real number

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

N-sphere and Real number · Orthogonal group and Real number · See more »

Real projective line

In geometry, a real projective line is an extension of the usual concept of line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity".

N-sphere and Real projective line · Orthogonal group and Real projective line · See more »

Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

N-sphere and Riemann sphere · Orthogonal group and Riemann sphere · See more »

Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

N-sphere and Simply connected space · Orthogonal group and Simply connected space · See more »

Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

N-sphere and Sphere · Orthogonal group and Sphere · See more »

Symplectic group

In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted and, the latter is called the compact symplectic group.

N-sphere and Symplectic group · Orthogonal group and Symplectic group · See more »

3-sphere

In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.

3-sphere and N-sphere · 3-sphere and Orthogonal group · See more »

The list above answers the following questions

N-sphere and Orthogonal group Comparison

N-sphere has 68 relations, while Orthogonal group has 178. As they have in common 16, the Jaccard index is 6.50% = 16 / (68 + 178).

References

This article shows the relationship between N-sphere and Orthogonal group. To access each article from which the information was extracted, please visit:

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