Similarity to Symmetric Matrices over Fields Which are not Formally Real.
CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES
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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.
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