  We discuss the linearization of vector-spinor (spin-3/2) nonlinear
supersymmetry (vsNLSUSY) transformations for both $N = 1$ and $N$-extended SUSY
in flat spacetime based on the commutator algebra by using functionals
(composites) of spin-3/2 Nambu-Goldstone (NG) fermions, which are expressed as
simple products of powers of the spin-3/2 NG fermions and a fundamental
determinant in the vsNLSUSY theory. We define basic component fields by means
of those functionals in a linearized vsSUSY theory including spin-3/2 fields,
general auxiliary ones and a $D$-term. The general forms of linear (rigid)
vsSUSY transformations for the component fields are determined uniquely from
the commutator-based linearization procedure. By considering appropriate
recombinations of the functionals of the spin-3/2 NG fermions for $N = 1$ SUSY,
we find that variations of the recombinations under the vsNLSUSY
transformations include linear spin-1/2 SUSY ones of spin-(3/2, 1) fields with
$U(1)$ gauge invariance. The spinorial gauge invariance of the Rarita-Schwinger
action in the linearization process is also discussed together with the $U(1)$
gauge invariance.
