Recent work of Samadi et al. introduced the fair PCA problem where the goal is to find a projection that minimizes the error and furthermore the error is balanced across two groups in the population. The takeaway message from their paper was that adding one extra dimension is enough. Firstly, this paper resolves the main open question from the work of Samadi et al. by giving an algorithm that does not need to increase the dimension by one. Second, they push the framework fo fair PCA in some interesting new directions that allow for alternative notions of fairness and multiple groups. They improve the fairness penalty to be \sqrt{k} from k-1. The reviewers felt that the paper gives a compelling collection of results on an important topic.