  Via supersymmetry argument, we determine the effective action of the SU(2)
supersymmetric Yang-Mills quantum mechanics up to two constants, which results
from the full supersymmetric completion of the F^4 term. The effective action,
consisting of zero, two, four, six and eight fermion terms, agrees with the
known perturbative one-loop calculations from the type II string theory and the
matrix theory. Our derivation thus demonstrates its non-renormalization
properties, namely, the one-loop exactness of the aforementioned action and the
absence of the non-perturbative corrections. We briefly discuss generalizations
to other branes and the comparison to the DLCQ supergravity analysis. In
particular, our results show that the stringent constraints from the
supersymmetry are responsible for the agreement between the matrix theory and
supergravity with sixteen supercharges.
