  As a promising candidate technology for the next-generation wireless
communications, reconfigurable intelligent surface (RIS) has gained tremendous
research interest in both the academia and industry in recent years. Only
limited knowledge, however, has been obtained about the channel eigenvlaue
characteristics and degrees of freedom (DoF) of systems containing RISs. In
this paper, we focus on a wireless communication system where both the
transmitter and receiver are respectively equipped with an RIS. Features of
eigenvalues, such as their summation and individual behavior, are investigated
for both the correlation matrix of an RIS and the composite channel matrix
encompassing the two RISs and the wireless channel. Furthermore, the concept of
effective degrees of freedom (EDoF), i.e., the number of subchannels actively
contributing to conveying information, is revisited for RIS-enabled systems.
Analytical and numerical results demonstrate that the EDoF depends upon various
factors including the operating SNR, physical parameters of RISs, and
propagation environment.
