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Let Q(t) be a matrix, function of time, t. Assume that Q is orthogonal for all...

Let Q(t) be a matrix, function of time, t. Assume that Q is orthogonal for all t. Show that if Q(t_0) = I (identity matrix) for some t_0 then d/dt (Q(t_0)) is skew-symmetric.

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Answer #1

The solution is given below. I have used the fact that since the derivative of a matrix is just the derivative of each entry assembled in a matrix. The solution follows by using the definitions of orthogonal and skew symmetric.

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