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May 24, 2012 at 12:50 comment added Julien Maubon Thanks for the answer, this is indeed one of the paper I saw after reading Noah's comment. I may be missing something but I think Oeding addresses a different problem. He wants to prescribe all the principal minors of a symmetric matrix, whereas I want to prescribe only the 2x2 principal minors, but of a positive semidefinite matrix, as you pointed. If we drop the positive semidefinite condition then it's always possible to prescribe the 2x2 principal minors. See George Lowther comment and Edit 2 in the question.
May 23, 2012 at 23:22 history answered Igor Rivin CC BY-SA 3.0