The LIGO/Virgo gravitational-wave (GW) interferometers have to-date detected ten merging black hole (BH) binaries, some with masses considerably larger than had been anticipated. Stellar-mass BH binaries at the high end of the observed mass range (with chirp mass ${cal M} gtrsim 25 M_{odot}$) should be detectable by a space-based GW observatory years before those binaries become visible to ground-based GW detectors. This white paper discusses some of the synergies that result when the same binaries are observed by instruments in space and on the ground. We consider intermediate-mass black hole binaries (with total mass $M sim 10^2 -10^4 M_{odot}$) as well as stellar-mass black hole binaries. We illustrate how combining space-based and ground-based data sets can break degeneracies and thereby improve our understanding of the binarys physical parameters. While early work focused on how space-based observatories can forecast precisely when some mergers will be observed on the ground, the reverse is also important: ground-based detections will allow us to dig deeper into archived, space-based data to confidently identify black hole inspirals whose signal-to-noise ratios were originally sub-threshold, increasing the number of binaries observed in both bands by a factor of $sim 4 - 7$.
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