Similarity to Symmetric Matrices over Fields Which are not Formally Real.

Abstract

It is shown that a matrix is similar to a symmetric matrix over a field of characteristic 2 if and only if the minimum polynomial of the matrix is not the product of distinct irreducible polynomials whose splitting fields are inseparable extensions. When the field is not characteristic 2, a known theorem is generalized by considering k, the number of elementary divisors of odd degree of the nxn matrix A: If -1 is a sum of (2 sup nu) squares and n differs from a multiple of 2 sup(nu + 1) by at most plus or minus k, then A is similar to a symmetric matrix.

Document Details

Document Type
Technical Report
Publication Date
Jun 16, 1974
Accession Number
ADA009807

Entities

People

  • Edward A. Bender
  • J. V. Brawley Jr

Organizations

  • Clemson University

Tags

DTIC Thesaurus Topics

  • Polynomials
  • Splitting

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.