from ?eigen

symmetric: if 'TRUE', the matrix is assumed to be symmetric (or
          Hermitian if complex) and only its lower triangle is used. If
          'symmetric' is not specified, the matrix is inspected for
          symmetry.


I think that could mislead a naive reader as it suggests that, with 
symmetric=TRUE,
the result of eigen() (vectors and values) depends only on the lower-triangular 
values, 
and thus not on the values on the diagonal (that's not true for the 
eigenvalues).

I suggest that changing it to 

"... and only its lower triangle is used when computing the eigenvectors."

would be more accurate, perhaps even with a reminder about the trace - sum of 
eigenvalues
relationship.

Dan

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