# Accession Number:

## ADA009807

# Title:

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

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1974-06-16

# Pagination or Media Count:

## 16.0

# 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 supnu 1 by at most plus or minus k, then A is similar to a symmetric matrix.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics