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January 1, 1956Mathematical Proceedings of the Cambridge Philosophical Society791 citations

On best approximate solutions of linear matrix equations

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RPRoger Penrose

Key Points

  • This research aims to explore the application of a generalized inverse for solving inconsistent linear matrix equations using least squares.
  • Defines a unique generalization of the inverse for any non-singular matrix.
  • Applies the method of least squares to find approximate solutions for inconsistent systems.
  • Suggests computational techniques for obtaining the generalized inverse.
  • Provides a framework for effectively addressing the statistical problem of inconsistent equations.
  • Demonstrates the utility of the generalized inverse in improving solution accuracy.

Abstract

In an earlier paper (4) it was shown how to define for any matrix a unique generalization of the inverse of a non-singular matrix. The purpose of the present note is to give a further application which has relevance to the statistical problem of finding ‘best’ approximate solutions of inconsistent systems of equations by the method of least squares. Some suggestions for computing this generalized inverse are also given.

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Cite This Study

Roger Penrose (1956) studied this question.

synapsesocial.com/papers/6a090b112757fd3263d3abf0https://doi.org/10.1017/s0305004100030929
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