I read this sentence.
Suppose that the matrix $A_{ij}$ of dimension $n_i \times n_j$ has rank $k$ to precision $\epsilon$, then there exists a factorization of $A_{ij}$ of the form: $A_{ij} = L_i S_{ij} R_j + \text{O}(\epsilon)$.
I wonder what does matrix rank $k$ to precision $\epsilon$ mean?
Thank you.