I have a question for the algorithm gen public key of The Goldreich–Goldwasser–Halevi (GGH) lattice-based cryptosystem. GenKey Algorithm as described in the paper:
Pick a matrix $R'$ which is uniformly distributed in $\{-l,\ldots,l\}$ and then compute $R = R' + k\cdot I$. Then we have $R$ a private basis. And $I$ know a basis of the lattice is linearly independent vectors.
I want to know why $R$ is the basis of lattice when it maybe isn't linearly independent vectors?