In mathematics, a rule for changing one geometric figure (or matrix or vector ) into another using a formula with a specified format.
The format must be a linear combination, in which the original components (e.g., the x and y coordinates of each point of the original figure) are changed via the formula a x + b y to produce the coordinates of the transformed figure. Examples include flipping the figure over the x or y axis, stretching or compressing it, and rotating it. Every such transformation has an inverse, which undoes its effect.