  In this work, we consider both channel estimation and reflection design
problems in point-to-point reconfigurable intelligent surface (RIS)-aided
millimeter-wave (mmWave) MIMO communication systems. First, we show that by
exploiting the low-rank nature of mmWave MIMO channels, the received training
signals can be written as a low-rank multi-way tensor admitting a canonical
polyadic CP decomposition. Utilizing such a structure, a tensor-based RIS
channel estimation method (termed TenRICE) is proposed, wherein the tensor
factor matrices are estimated using an alternating least squares method. Using
TenRICE, the transmitter-to-RIS and the RIS-to-receiver channels are
efficiently and separately estimated, up to a trivial scaling factor. After
that, we formulate the beamforming and RIS reflection design as a spectral
efficiency maximization problem. Due to its non-convexity, we propose a
heuristic non-iterative two-step method, where the RIS reflection vector is
obtained in a closed form using a Frobenius-norm maximization (FroMax)
strategy. Our numerical results show that TenRICE has a superior performance,
compared to benchmark methods, approaching the Cram\'er-Rao lower bound with a
low training overhead. Moreover, we show that FroMax achieves a comparable
performance to benchmark methods with a lower complexity.
