Adding a conditional conjugateIf<bool>() method would allow to simplify the implementation of some of our solver code. For instance, in PartialPivLU, we have code like:

  if (Conjugate) {
    dst = m_lu.template triangularView<Upper>().adjoint().solve(rhs);
    m_lu.template triangularView<UnitLower>().adjoint().solveInPlace(dst);
  } else {
    dst = m_lu.template triangularView<Upper>().transpose().solve(rhs);
    m_lu.template triangularView<UnitLower>().transpose().solveInPlace(dst);
  }

that could be factorized as:

  dst = m_lu.template triangularView<Upper>().transpose()
            .template conjugateIf<Conjugate>().solve(rhs);
  m_lu.template triangularView<UnitLower>().transpose()
      .template conjugateIf<Conjugate>().solveInPlace(dst);

More complicated exemples include FullPivLU::_solve_impl_transposed, and some code in PR567: https://bitbucket.org/eigen/eigen/pull-requests/567/restructuring-of-all-densesolvers/diff

We could keep it internal:

  dst = internal::conj_if<bool>(m_lu.template triangularView<Upper>().transpose()).solve(rhs);

but (1) it's less readable than as a free function, and (2) if it's good for us, it's probably good for our users too.