Abstract
In 1936 Eckart and Young formulated the problem of approximating a specific matrix of specific rank. This has come to be known as the Eckart-Young theorem. It has important applications to factor analysis in psychometrics (for which it was originally developed by Eckart and Young), to clustering and aggregation in econometrics, to quantum chemistry, as well as to the theory of biased estimation in statistics. This chapter discusses the formulation and solution of the problem of approximating a specific matrix of specific rank. It also provides a proof of the Eckart-Young theorem so as to solve the specific matrix of specific rank.
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