# How to Compute the EOFs by SVD?

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Considering I have a matrix ##\mathbf{A}## which has a size of ##M \times N##, how can I compute the Empirical Orthogonal Functions (EOFs) by Singular Value Decomposition (SVD)?

According to SVD, the matrix ##\mathbf{A}## is

##\mathbf{A} = \mathbf{U} \mathbf{\Sigma} \mathbf{V}^{T}##

where a superscript of ##T## denotes a transpose. Now, which are the EOFs in this equation, are they the rows of ##\mathbf{V}^{T}## or its columns (the rows of ##\mathbf{V}##)?