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The singular value decomposition (SVD) of a matrix is a fundamental tool in computer science, data analysis, and statistics. It's used for all kinds of applications from regression to prediction, to finding approximate solutions to optimization problems. In this series of two posts we'll motivate, define, compute, and use the singular value decomposition to analyze some data. (Jump to the second post) I want to spend the first post entirely on motivation and background.
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Some systems of equations do not have a unique solution, but we can find an approximate solution using the method of least squares. Applications of this method include linear and polynomial regression.
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