  We study localization of five-dimensional supersymmetric $U(1)$ gauge theory
on $\mathbb{S}^3 \times \mathbb{R}_{\theta}^{2}$ where
$\mathbb{R}_{\theta}^{2}$ is a noncommutative (NC) plane. The theory can be
isomorphically mapped to three-dimensional supersymmetric $U(N \to \infty)$
gauge theory on $\mathbb{S}^3$ using the matrix representation on a separable
Hilbert space on which NC fields linearly act. Therefore the NC space
$\mathbb{R}_{\theta}^{2}$ allows for a flexible path to derive matrix models
via localization from a higher-dimensional supersymmetric NC $U(1)$ gauge
theory. The result shows a rich duality between NC $U(1)$ gauge theories and
large $N$ matrix models in various dimensions.
