Unformatted text preview: trices with determinant 1 (which is a group of order 4) and the cyclic group of order 3 generated by the permutation matrix R D 2 4 0 0 1 1 0 0 0 1 0 3 5 . 4.1.5. (a) If T denotes the group of rotation matrices for the tetrahedron and S is any rotation matrix for the cube that is not contained in T , show that the group of rotation matrices for the cube is T [ T s . (b) Show that the group of rotation matrices for the cube consists of signed permutation matrices with determinant 1, that is, matrices with entries in f 0; ˙ 1 g with exactly one nonzero entry in each row and in each column, and with determinant 1. (c) Show that the group of rotation matrices for the cube is the semidirect product of the group V consisting of diagonal permutation matrices with determinant 1 (which is a group of order 4) and the group of 3–by–3 permutation matrices....
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 Fall '08
 EVERAGE
 Algebra, Matrices, rotation matrices

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