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Psychometrika

, Volume 1, Issue 3, pp 211–218 | Cite as

The approximation of one matrix by another of lower rank

  • Carl Eckart
  • Gale Young
Article

Abstract

The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matrices in a canonic form. It is found that the problem always has a solution which is usually unique. Several conclusions can be drawn from the form of this solution.

A hypothetical interpretation of the canonic components of a score matrix is discussed.

Keywords

Public Policy Statistical Theory Lower Rank Canonic Form Mathematical Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Psychometric Society 1936

Authors and Affiliations

  • Carl Eckart
    • 1
  • Gale Young
    • 1
  1. 1.University of ChicagoChicago

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