[linear transformation] n (ca. 1889) 1: a transformation in which the new variables are linear functions of the old variables
2: a function that maps the vectors of one vector space onto the vectors of the same or another vector space with the same field of scalars in such a way that the image of the sum of two vectors equals the sum of their images and the image of the product of a scalar and a vector equals the product of the scalar and the image of the vector