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In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, "connected with") between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation:x mapsto A x+ b.In the finite-dimensional case each affine transformation is given by a matrix A and a vector b, satisfying certain properties described below.Geometrically, an affine transformation in Euclidean space is one that preserves