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Unformatted text preview: ) and show that it is invariant. 6. Let SO (3) be the set of 3 3 orthogonal matrices with determinant +1. The tangent space of SO (3) at the identity is given by the set of skew-symmetric matrices of the form b = ( ) = - 3 2 3- 1- 2 1 (well show this later in the course). (a) Show that if v R 3 , b v = v , where is the cross product in R 3 . (b) Show that the tangent space T R SO (3) consists of matrices of the form b R where b is skew-symmetric. (c) Show that the ow of a vector eld g ( R ) = b R is given by t ( R ) = exp( b t ) R where exp is the matrix exponential....
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- Fall '08