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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 with an example from image processing.

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The Singular Value Decomposition

  • 章节

  • 发表日期：

    2025年

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  • Jörg Liesen,
  • Volker Mehrmann

摘要

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 with an example from image processing.