Rayleigh fading channel as a scalar quantity
Rayleigh channel is defined between transmit and receive antennas, if there is one transmit and one receive antennas then there is one Rayleigh fading coefficient.

If there is one transmit and multiple receive antennas then there is a vector or fading channel.

If there is one receive  and multiple antennas then there is a vector or fading channel.

If there are multiple trasmit and receive antennas then you have a Rayleigh fading matrix represting the wireless channel