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A circle-preserving transformation composed of an odd number of inversions.

A group of sociable numbers of order 3.

An area-preserving affine transformation. Equiaffinities include the crossed hyperbolic rotation, elliptic rotation, hyperbolic rotation, and parabolic rotation.

A circle-preserving transformation composed of an even number of inversions.

An operator L^~ is said to be linear if, for every pair of functions f and g and scalar t, L^~(f+g)=L^~f+L^~g and L^~(tf)=tL^~f.

The product of any number of perspectivities.

The property of being the only possible solution (perhaps modulo a constant, class of transformation, etc.).

A conjugate matrix is a matrix A^_ obtained from a given matrix A by taking the complex conjugate of each element of A (Courant and Hilbert 1989, p. 9), i.e., ...

A similarity transformation which transforms each line to a parallel line whose length is a fixed multiple of the length of the original line. The simplest dilation is ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...