Undergrad Which Are the EOFs in SVD?

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SUMMARY

The Empirical Orthogonal Functions (EOFs) in Singular Value Decomposition (SVD) are identified as the columns of the matrix ##\mathbf{V}##, which corresponds to the rows of ##\mathbf{V}^{T}##. In the context of a matrix ##\mathbf{A}## of size ##M \times N##, the SVD is expressed as ##\mathbf{A} = \mathbf{U} \mathbf{\Sigma} \mathbf{V}^{T}##. This clarification is crucial for accurately computing EOFs in various applications, particularly in fields such as data analysis and climate modeling.

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  • Understanding of Singular Value Decomposition (SVD)
  • Familiarity with matrix notation and operations
  • Knowledge of Empirical Orthogonal Functions (EOFs)
  • Basic concepts in linear algebra
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  • Explore applications of Empirical Orthogonal Functions (EOFs) in climate data analysis
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Researchers, data scientists, and climate modelers who require a solid understanding of EOFs and SVD for data analysis and interpretation in their respective fields.

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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}##)?

Thank you in advance.
 
Hi there. The EOFs are the columns of V^T.

This site helps me to figure this out https://pmc.ucsc.edu/~dmk/notes/EOFs/EOFs.html. Goodnight from your atemporal interested in orthostatics guy.

Mod note: deleted broken link
 
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