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