Abstract
The matrix decomposition introduced in this chapter is very important in many practical applications, since it yields the best possible approximation (in a certain sense) of a given matrix by a matrix of low rank. A low rank approximation can be considered a “compression” of the data represented by the given matrix. We illustrate this below with an example from image processing.
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Notes
- 1.
In the development of this decomposition from special cases in the middle of the 19th century to its current general form many important players of the history of Linear Algebra played a role. In the historical notes concerning the singular value decomposition in [HorJ91] one finds contributions of Jordan (1873), Sylvester (1889/1890) and Schmidt (1907). The current form was shown in 1939 by Carl Henry Eckart (1902–1973) and Gale Young .
- 2.
We thank Falk Ebert for his help. The original bear can be seen in front of the Mathematics building of the TU Berlin. More information on Matheon can be found at www.matheon.de.
- 3.
Eliakim Hastings Moore (1862–1932) and Sir Roger Penrose (1931–).
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Liesen, J., Mehrmann, V. (2015). The Singular Value Decomposition. In: Linear Algebra. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-24346-7_19
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DOI: https://doi.org/10.1007/978-3-319-24346-7_19
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