Cayley Transform

In mathematics, the Cayley transform, named after Arthur Cayley, has a cluster of related meanings. As originally described by Cayley (1846), the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. In complex analysis, the Cayley transform is a conformal mapping (Rudin 1987) in which the image of the upper complex half-plane is the unit disk (Remmert 1991, pp. 82ff, 275). And in the theory of Hilbert spaces, the Cayley transform is a mapping between linear operators (Nikol’skii 2001).