Hmm. If you want to be very math-pedantic - vectors and tensors are described or parameterized with n-D arrays of scalar values, but they're actually mathematical objects in their own right. Given different frames, sets of basis vectors, or changing frames and basis vectors, there are sets of transforms that you use to get from one to the other.
Depending on what frame you are in, d/dt {velocity vector} isn't always {dvx/dt,dvy/dt,dvz/dt} like you would expect for a pure array.
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