  With the discovery of the black hole binary (BBH) coalescence GW150914 the
era of gravitational-wave (GW) astronomy has started. It has recently been
shown that BBH with masses comparable to or higher than GW150914 would be
visible in the eLISA band a few years before they finally merge in the band of
ground-based detectors. This would allow for pre-merger electromagnetic alerts,
dramatically increasing the chances of a joint detection, if BBH are indeed
luminous in the electromagnetic band. In this paper we explore a quite
different aspect of multi-band GW astronomy, and verify if, and to what extent,
measurement of masses and sky position with eLISA could improve parameter
estimation and tests of general relativity with ground-based detectors. We
generate a catalog of 200 BBH and find that having prior information from eLISA
can reduce the uncertainty in the measurement of source distance and primary
black hole spin by up to factor of 2 in ground-based GW detectors. The
component masses estimate from eLISA will not be refined by the ground based
detectors, whereas joint analysis will yield precise characterization of the
newly formed black hole and improve consistency tests of general relativity.
