  The restricted isometry property (RIP) is essential for the linear map to
guarantee the successful recovery of low-rank matrices. The existing works show
that the linear map generated by the measurement matrices with independent and
identically distributed (i.i.d.) entries satisfies RIP with high probability.
However, when dealing with non-i.i.d. measurement matrices, such as the
rank-one measurements, the RIP compliance may not be guaranteed. In this paper,
we show that the RIP can still be achieved with high probability, when the
rank-one measurement matrix is constructed by the random unit-modulus vectors.
Compared to the existing works, we first address the challenge of establishing
RIP for the linear map in non-i.i.d. scenarios. As validated in the
experiments, this linear map is memory-efficient, and not only satisfies the
RIP but also exhibits similar recovery performance of the low-rank matrices to
that of conventional i.i.d. measurement matrices.
