The reviewers found that this paper was useful for the field, offering a new method for aligning multi-site fMRI data, with some disagreement. One of the main concerns was about the clarity of the paper which greatly impacts its usefulness. Please improve the quality of the writing for the final draft. There is a major typo in the paper: everywhere XX^T is mentioned, I think you mean X^TX (the identify matrices are also wrongly subscripted). In fact R1's comment is right, XX^T is likely not singular given V>>T.