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Jul 16, 2019 at 11:31 comment added YCor It's true, for both symmetric and skew-symmetric matrices, over an arbitrary field (and also hermitian...), and known as "Principal minor theorem". For a generalization, see Theorem 2.9 here (V. Kodiyalam, T. Lam, R. Swan, Determinantal ideals, Pfaffian ideals, and the principal minor theorem. Noncommutative rings, group rings, diagram algebras and their applications, 35-60, Contemp. Math., 456, Amer. Math. Soc., Providence, RI, 2008). I haven't found a more classical reference.
Jul 12, 2010 at 4:07 vote accept Leo
Apr 22, 2010 at 22:11 answer added David E Speyer timeline score: 3
Apr 22, 2010 at 14:06 answer added damiano timeline score: 11
Apr 22, 2010 at 12:53 history asked Leo CC BY-SA 2.5