Singular Value Decomposition

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The Singular Value Decomposition (SVD) is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. Using the SVD, we can determine the rank of matrix, quantify the sensitivity of a linear system to numerical error, or obtain an optimal lower-rank approximation to the matrix. Our interest in the SVD, from the point of view of learning dynamical systems, is its ability to split a vector space into lower-dimensional subspaces

The mini tutorial on the SVD provides a quick introduction to the definition and properties of the SVD, as well as a listing of some applications in which the SVD is used.

For further information on the Singular Value Decomposition, you may wish to consult any of the following books:

  SVD and Signal Processing: Algorithms, Analysis and Applications, edited 
  by Ed. F. Deprettere, Elsevier Science Publishers, North Holland, 1988.

  SVD and Signal Processing II: Algorithms, Analysis and Applications, edited 
  by R. Vaccaro, Elsevier Science Publishers, North Holland, 1991.

  Computer Methods for Mathematical Computations, by George E. Forsythe, 
  Michael A. Malcolm, and Cleve B. Moler, Prentice Hall, 
  Englewood Cliffs, New Jersey, 1977, pg 201-235.
  Matrix Computations, by Gene H. Golub and Charles F. van Loan,
  John Hopkins University Press, Baltimore, Maryland, 1983, pg 16-21, 293

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