  The standard goal for an effective algebraic multigrid (AMG) algorithm is to
develop relaxation and coarse-grid correction schemes that attenuate
complementary error modes. In the nonsymmetric setting, coarse-grid correction
$\Pi$ will almost certainly be nonorthogonal (and divergent) in any known
standard product, meaning $\|\Pi\| > 1$. This introduces a new consideration,
that one wants coarse-grid correction to be as close to orthogonal as possible,
in an appropriate norm. In addition, due to non-orthogonality, $\Pi$ may
actually amplify certain error modes that are in the range of interpolation.
Relaxation must then not only be complementary to interpolation, but also
rapidly eliminate any error amplified by the non-orthogonal correction, or the
algorithm may diverge. This paper develops analytic formulae on how to
construct ``compatible'' transfer operators in nonsymmetric AMG such that
$\|\Pi\| = 1$ in some standard matrix-induced norm. Discussion is provided on
different options for the norm in the nonsymmetric setting, the relation
between ``ideal'' transfer operators in different norms, and insight into the
convergence of nonsymmetric reduction-based AMG.
