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A minor is principal means it is defined by the same row and column indices. We study ideals generated by principal minors of size t ≤ n of a generic n × n matrix X, in the polynomial ring generated over an algebraically closed field by the entries of X. When t = 2 the resulting quotient ring is a normal complete intersection domain. We show for any t, upon inverting det X the ideals given respectively by the size t and the size n − t principal minors become isomorphic. From that we show the algebraic set given by the size n − 1 principal minors has a codimension 4 component defined by the determinantal ideal, plus a codimension n component. When n = 4 the two components are linked, and in fact, geometrically linked.

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