Page 674 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Operator Standard Matrix Effect on the Unit Square
Reflection about the y-axis

Reflection about the x-axis

Reflection about the line
Counterclockwise rotation through an angle θ

In Section 4.2 we discussed reflections, projections, rotations, contractions, and dilations of . We shall now consider some other
basic linear operators on .

Compressions and Expansions

If the x-coordinate of each point in the plane is multiplied by a positive constant k, then the effect is to compress or expand each

plane figure in the x-direction. If , the result is a compression, and if , it is an expansion (Figure 9.2.2). We call such

an operator a compression (or an expansion) in the x-direction with factor k. Similarly, if the y-coordinate of each point is

multiplied by a positive constant k, we obtain a compression (or expansion) in the y-direction with factor k. It can be shown that

compressions and expansions along the coordinate axes are linear transformations.

Figure 9.2.2