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N-sphere and Quaternionic projective space

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

Difference between N-sphere and Quaternionic projective space

N-sphere vs. Quaternionic projective space

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension. In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by and is a closed manifold of (real) dimension 4n.

Similarities between N-sphere and Quaternionic projective space

N-sphere and Quaternionic projective space have 7 things in common (in Unionpedia): Circle group, Hopf fibration, Mathematics, Möbius transformation, Riemann sphere, Sphere, Symplectic group.

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 Quaternionic projective space · See more »

Hopf fibration

In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.

Hopf fibration and N-sphere · Hopf fibration and Quaternionic projective space · 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 Quaternionic projective space · See more »

Möbius transformation

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

Möbius transformation and N-sphere · Möbius transformation and Quaternionic projective space · 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 · Quaternionic projective space and Riemann sphere · 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 · Quaternionic projective space 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 · Quaternionic projective space and Symplectic group · See more »

The list above answers the following questions

N-sphere and Quaternionic projective space Comparison

N-sphere has 68 relations, while Quaternionic projective space has 33. As they have in common 7, the Jaccard index is 6.93% = 7 / (68 + 33).

References

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

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