suppose sigma = [[1/2, -sqrt(3)/2, sqrt(3/2)] [-sqrt(3)/2, 3/2, 1/2] [sqrt(3)/2, 1/2, 0]] is a symmetric second order tensor with matrix given referring to the unprimed coordinate system. Find sigma' the matrix referring to the prime coordinate system.

In the previous problem we found a matrix A when multipled by a 1x3 matrix in the unprimed coordinate system you would get a 1x3 matrix in the prime coordinate system.

This is where I am confused.

Does sigma' = A (tensor product) sigma? meaning I would have a 9x9 matrix.

or is sigma' =A times sigma? leaving me with a 3x3 matrix?

(A was a 3x3 matrix)

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Figured out it was the second option and not a tensor product.