  In this paper, we study the theories with SU(2|4) symmetry which consist of
the plane wave matrix model (PWMM), super Yang-Mills theory (SYM) on RxS^2 and
SYM on RxS^3/Z_k. The last two theories can be realized as theories around
particular vacua in PWMM, through the commutative limit of fuzzy sphere and
Taylor's T-duality. We apply the localization method to PWMM to reduce the
partition function and the expectation values of a class of supersymmetric
operators to matrix integrals. By taking the commutative limit and performing
the T-duality, we also obtain the matrix integrals for SYM on RxS^2 and SYM on
RxS^3/Z_k. In this calculation, we ignore possible instanton effects and our
matrix integrals describe the perturbative part exactly. In terms of the matrix
integrals, we also provide a nonperturbative proof of the large-N reduction for
circular Wilson loop operator and free energy in N=4 SYM on RxS^3.
