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Eulerian graphs and polynomial identities for sets of matrices.

J P Hutchinson1

  • 1University of Pennsylvania, Philadelphia, Pennsylvania 19104.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1974
PubMed
Summary

This study determines the minimum standard identity for skew-symmetric matrices. The findings are relevant to understanding algebraic structures in linear algebra.

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Area of Science:

  • Abstract algebra
  • Linear algebra
  • Matrix theory

Background:

  • Standard identities are fundamental in understanding polynomial properties.
  • Skew-symmetric matrices have unique structural properties.
  • The study of identities over fields of characteristic 0 is a key area in algebra.

Purpose of the Study:

  • To determine the minimum standard identity for n x n skew-symmetric matrices.
  • To contribute to the theory of polynomial identities in matrix algebras.

Main Methods:

  • Utilizing the definition of standard identities.
  • Applying concepts of skew-symmetric matrices.
  • Working over a field of characteristic 0.

Main Results:

  • The minimum standard identity for the set of all n x n skew-symmetric matrices over a field of characteristic 0 was determined.
  • The specific form of this minimum identity is detailed.

Conclusions:

  • The research provides a precise characterization of a fundamental algebraic object.
  • This result advances the understanding of polynomial identities in the context of skew-symmetric matrices.

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