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Based on the solution of \textbf{Paulsen Problem} by Kwok, Lau, Lee, andRamachandran [\textit{STOC'18-Proceedings of the 50th Annual ACM SIGACTSymposium on Theory of Computing, 2018}] and independently by Hamilton, andMoitra [\textit{Isr. J. Math., 2021}] we study Paulsen Problem and ProjectionProblem in the context of Hilbert C*-modules. We show that for commutativeC*-algebras, if Modular Paulsen Problem has a solution, then Modular ProjectionProblem also has a solution. We formulate the problem of operator scaling formatrices over C*-algebras.

Modular Paulsen Problem and Modular Projection Problem