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Cayley transform

In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by Cayley (1846), the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. The transform is a homography used in real analysis, complex analysis, and quaternionic analysis. In the theory…

Art, Matrix map & Complex homography

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Real homography

Complex homography

Quaternion homography

Matrix map

Operator map

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Cayley transform

Nodes63
Edges62
Triples78
Avg. degree1.97
Density0.031746
Components1

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Cayley transform

Top relations

related to References · 54
Cayley transform → Academic Press ISBN, Applications, Applied Mathematics, Arthur, Arthur Cayley, Berberian, Cambridge University Press, Cayley, CRC Press ISBN, Debnath, Encyclopaedia, Functional Analysis, Graduate Texts, Hazewinkel, Helmberg, Hilbert Space, Hilbert Spaces, International Series, Introduction, ISBN
related to Operator map · 7
Cayley transform → An, Cayley, Here, Hilbert, However, See, So
related to Real homography · 6
Cayley transform → As, Cayley, For, Legendre, The Cayley, Thus
related to Complex homography · 5
Cayley transform → Cayley, Furthermore, Möbius, On, Since
related to Matrix map · 4
Cayley transform → Among, AT, Cayley, Then
is a · 2
Cayley transform → mapping between linear operators, mapping between skew-symmetric matrices and special orthogonal matrices

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Important terminology

transform cayley complex displaystyle matrix matrices real homography orthogonal skew-symmetric mapping isbn mathematics -1 cos sin rotation one described special

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cayley transformis amapping between skew-symmetric matrices and special orthogonal matrices0.90text
Cayley transformis amapping between linear operators0.90text
Cayley transformrelated to Complex homographyOn0.60section
Cayley transformrelated to Complex homographyCayley0.60section
Cayley transformrelated to Complex homographySince0.60section
Cayley transformrelated to Complex homographyMöbius0.60section
Cayley transformrelated to Complex homographyFurthermore0.60section
Cayley transformrelated to Matrix mapAmong0.60section
Cayley transformrelated to Matrix mapAT0.60section
Cayley transformrelated to Matrix mapThen0.60section
Cayley transformrelated to Matrix mapCayley0.60section
Cayley transformrelated to Operator mapAn0.60section

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