In Gaussian optics magnification is a scalar; the interpretation is obvious.  In linear optics, the simplest optics of astigmatic systems, the generalization is a  2 2×  real matrix and, in general, is much harder to interpret.  This generalized magnification may imply magnification in the familiar sense that differs from one meridian to another, shear distortion, rotation, reflection, inversion, magnification in the familiar sense or combinations of these effects.  The purpose of this paper is to illustrate generalized magnification and to provide a comprehensive interpretation.  Because the treatment is abstract it can be applied to blur and size magnification and to any magnification that can be represented by a  2 X 2  matrix. (S Afr Optom 2010 69(3) 109-122)