What is "collineation"

Collineation \Col*lin`e*a"tion\, n. [L. collineare to direct in a straight line. See Collimation.] The act of aiming at, or directing in a line with, a fixed object. [R.]
--Johnson.

n. 1 The act of collineate; collimation. 2 (cx algebra English) An isomorphism from one projective space to another, often to itself.

In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a group, called the collineation group.