This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 2 . (d) Show that any rotation matrix R is a product of two reection matrices. 4.4.5. Show that an element of SO . 3 ; R / is a product of two reection matrices. A matrix of a rotationreection is a product of three reection matrices. Thus any element of O . 3 ; R / is a product of at most three reection matrices. 4.5. The Full Symmetry Group and Chirality All the geometric gures in threedimensional space that we have considered the polygonal tiles, bricks, and the regular polyhedra admit reection symmetries. For reasonable gures, every symmetry is implemented by by a linear isometry of R 3 ; see Proposition 1.4.1 . The rotation...
View Full
Document
 Fall '08
 EVERAGE
 Algebra

Click to edit the document details