Affine Function

Affine functions represent vector-valued functions of the form


The coefficients can be scalars or dense or sparse matrices. The constant term is a scalar or a column vector.

In geometry, an affine transformation or affine map (from the Latin, affinis, "connected with") between two vector spaces consists of a linear transformation followed by a translation. In a geometric setting, these are precisely the functions that map straight lines to straight lines.

See also

Affine, Affine Complex Plane, Affine Coordinates, Affine Equation, Affine Geometry, Affine Group, Affine Hull, Affine Plane, Affine Scheme, Affine Space, Affine Transformation, Affine Variety

This entry contributed by Alberto Gallini

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Cite this as:

Gallini, Alberto. "Affine Function." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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