  Dual complex numbers can represent rigid body motion in 2D spaces. Dual
complex matrices are linked with screw theory, and have potential applications
in various areas. In this paper, we study low rank approximation of dual
complex matrices. We define $2$-norm for dual complex vectors, and Frobenius
norm for dual complex matrices. These norms are nonnegative dual numbers. We
establish the unitary invariance property of dual complex matrices. We study
eigenvalues of square dual complex matrices, and show that an $n \times n$ dual
complex Hermitian matrix has exactly $n$ eigenvalues, which are dual numbers.
We present a singular value decomposition (SVD) theorem for dual complex
matrices, define ranks and appreciable ranks for dual complex matrices, and
study their properties. We establish an Eckart-Young like theorem for dual
complex matrices, and present an algorithm framework for low rank approximation
of dual complex matrices via truncated SVD. The SVD of dual complex matrices
also provides a basic tool for Principal Component Analysis (PCA) via these
matrices. Numerical experiments are reported.
