Singular Value Decomposition (SVD) and Polar Form

@inproceedings{Gallier2011SingularVD,
  title={Singular Value Decomposition (SVD) and Polar Form},
  author={J. Gallier},
  year={2011}
}
In this section we assume that we are dealing with a real Euclidean space E. Let \( f : E \rightarrow E \) be any linear map. In general, it may not be possible to diagonalize f. We show that every linear map can be diagonalized if we are willing to use two orthonormal bases. This is the celebrated singular value decomposition (SVD). A close cousin of the SVD is the polar form of a linear map, which shows how a linear map can be decomposed into its purely rotational component (perhaps with a… Expand
THE SINGULAR VALUE DECOMPOSITION AND LOW RANK APPROXIMATION
The purpose of this paper is to present a largely self-contained proof of the singular value decomposition (SVD), and to explore its application to the low rank approximation problem. We begin byExpand

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