eigenvalue decomposition in EnKF

lovingckw

hello everyone, I have a question about the eigenvalue decomposition in the EnKF algorism. The left handside of the equation is m*m matrix. γ is m*N matrix. In my understanding, the number of eigenvalues is equal to the order of square matrix m*m, which is m. Why the paper says it has N or less than N eigenvalues. Thank you.

HA'A'(τ)+γγ(τ)=Z∏Z(τ) (τ means transpose)

Paper says that "the rank of Z∏Z(τ) is less than or equal to N. Thus ∏ will have N or less none-zero eigenvalues".