## ABSTRACT

The flight simulator is an important part in the training of airplane pilots. It has a real cockpit, but what you see outside the windows is computer imagery. When you change the simulated position of your plane, the simulation software must recompute a new view of the terrain, clouds, or other aircraft. This is done through the application of 3D affine and linear maps. In an actual flight simulator, for each frame of the simulated scene, complex 3D computations are necessary, most of them consisting of the types of maps discussed in this chapter. We discuss 3D linear space and revisit the important concepts, such as the linearity property and linear independence. Basic operations, such as scaling, reflection, rotation, and projection are defined and described in terms of the determinant and action ellipsoid. An orthogonal projection construction is introduced. We illustrate combining 3D linear maps and the non-commutative property of matrix multiplication. An application of the influence of a linear map on normal vectors to geometry is introduced. A list of matrix rules is given at the end of the chapter. Sketches and figures illustrate the concepts.