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The spin-transfer-torque-driven (STT-driven) dynamics of a domain wall in an easy-axis rare-earth transition-metal ferrimagnet is investigated theoretically and numerically in the vicinity of the angular momentum compensation point $T_A$, where the net spin density vanishes. The particular focus is given on the unusual interaction of the antiferromagnetic dynamics of a ferrimagnetic domain wall and the adiabatic component of STT, which is absent in antiferromagnets but exists in the ferrimagnets due to the dominant coupling of conduction electrons to transition-metal spins. Specifically, we first show that the STT-induced domain-wall velocity changes its sign across $T_A$ due to the sign change of the net spin density, giving rise to a phenomenon unique to ferrimagnets that can be used to characterize $T_A$ electrically. It is also shown that the frequency of the STT-induced domain-wall precession exhibits its maximum at $T_A$ and it can approach the spin-wave gap at sufficiently high currents. Lastly, we report a numerical observation that, as the current density increases, the domain-wall velocity starts to deviate from the linear-response result, calling for a more comprehensive theory for the domain-wall dynamics in ferrimagnets driven by a strong current.