Unformatted text preview: However, there is a more thoughtful method to work this out that seriously reduces the necessary computation; this method is outlined in the Exercises. In the next section, we will develop a more general conceptual framework in which to place this exploration, which will allow us to understand the experimental observation that for both the brick and the square tile, the total number of symmetries is twice the number of rotations. We will also see, for example, that the product of two rotations matrices is again a rotation matrix, and the product of two matrices, each of which is a reﬂection or a rotation–reﬂection, is a rotation. Exercises 4.3 4.3.1. Verify the formula for the reﬂection J ˛ through the plane perpendicular to ˛ . 4.3.2. J ˛ is linear. Find its matrix with respect to the standard basis of R 3 . (Of course, the matrix involves the coordinates of ˛ .)...
View
Full Document
 Fall '08
 EVERAGE
 Algebra, Matrices, symmetries, square tile

Click to edit the document details