# transformation of coordinate systems by rotation

I am trying to convert a set of coordinates from ECEF (Earth Center Earth Fixed) to ENU (East North Up). The operation is performed by applying a rotation matrix as shown in: [http://en.wikipedia.org/wiki/Geodetic_system#From_ECEF_to_ENU][1]

The article shows that if you have a vector to convert, you apply th e rotation matrix and obtained the desired result as a vector. My question is: if you apply the same rotation matrix to a matrix of vectors do you have to perform any additional actions, or the multiplication will be sufficient? I am investigating source code where the conversion is performed like this:

result = RotationMatrix * MatrixToConvert * RotationMatrixTransposed

Does this make sense"?

Isn't in sufficient like this:

result = MatrixToConvert * RotationMatrix

Thank you

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you need to have the RotationMatrix at the left of the MatrixToConvert.$\begin{pmatrix} \cos(\theta) & -\sin(\theta)\\ \sin(\theta) & \cos(\theta) \end{pmatrix}\cdot\begin{pmatrix} x_1 & x_2\\ y_1 & y_2 \end{pmatrix}$ – Alex Oct 5 '12 at 12:39
But I do not need the transpose of the Rotation Matrix as well. right? – DDC Oct 5 '12 at 16:17
You can only multiply MatrixToConvert by RotationMatrixTransposed if you have exactly 3 vectors in your matrix of vectors, which doesn't make much sense. I believe you don't need the transposed Matrix – Alex Oct 5 '12 at 17:03