Principal minors, Part II: The principal minor assignment problem

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Principal minors, Part I: A method for computing all the principal minors of a matrix (2006, background): “…result as % % det(A([1, 3, 5],[1, 3, 5])) function [pminor] = getpm(pm, v) % The index into pm is simply the binary number with the v(i)’th bit set for each i. n = length(v); % length of vector containing indices of minor idx = 0; for i = 1:n idx = idx + bitshift(1,v(i)-1); end pminor = pm(idx);”
Hyperdeterminantal relations among symmetric principal minors (2006, background): “mine whether a given vector A∗ of length 2n is realizable as the vector of all principal minors of some n×n-matrix A. Very recently, Griﬃn and Tsatsomeros gave an algorithmic solution to this problem [6, 7]. Their work gives an algorithm, which, under a certain “genericity” condition, either outputs”