# 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
1 Citations
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

#### References

SHOWING 1-7 OF 7 REFERENCES
On the Early History of the Singular Value Decomposition
• G. Stewart
• Mathematics, Computer Science
• SIAM Rev.
• 1993
This paper surveys the contributions of five mathematicians who were responsible for establishing the existence of the singular value decomposition and developing its theory. Expand
Applied Numerical Linear Algebra
The symmetric Eigenproblem and singular value decomposition and the Iterative methods for linear systems Bibliography Index. Expand
Mathematical foundations of elasticity
• Mathematics
• 1982
[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians,Expand
Introduction to applied mathematics
• Engineering
• 1986
Introduction to applied mathematics , Introduction to applied mathematics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
Matrix computations