Let x1, x2, x3 ER and 0 -x3 x2 X = x3 0 -x1 =-XT -22...

 

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Let x1, x2, x3 ER and 0 -x3 x2 X = x3 0 -x1 =-XT -22 x1 0 The set of all such matrices forms a vectorspace (called so(3)). Exponentiating matrices X = so(3) produces matrices exp(X) = SO(3). If the V operator is defined such that where x = x 21 x= x2 x3 prove for any RE SO(3), regardless of whether or not R = exp(X), that (RXRT) = Rx. Hint: divide R and RT into columns and rows. Let x1, x2, x3 ER and 0 -x3 x2 X = x3 0 -x1 =-XT -22 x1 0 The set of all such matrices forms a vectorspace (called so(3)). Exponentiating matrices X = so(3) produces matrices exp(X) = SO(3). If the V operator is defined such that where x = x 21 x= x2 x3 prove for any RE SO(3), regardless of whether or not R = exp(X), that (RXRT) = Rx. Hint: divide R and RT into columns and rows.