On certain Aggregates of Determinant Minors

Extract

Two curious identities have been established regarding certain aggregates of minors of special determinants; the first, which concerns axisymmetric determinants, having been discovered by Kronecker in 1882, and the second, which concerns centrosymmetric determinants, having been published by me in 1888, When we come to think of the possibility of generalising these identities, it is readily seen that there are at least two lines of attack which suggest, themselves on reading the mere description of the kind of identity; for, in saying that the identities deal with “an aggregate of minor determinants of a special determinant,” we are conscious of two points of limitation in the description, the one signalised by the word “minor” and the other by the word “special.” If, therefore, an identity were obtained regarding an aggregate of which the terms were determinantsunrestricted by a family relationship, we might have one form of generalisation; and if, while retaining the family relationship, we succeeded in removing the restriction as to the form of the parent, a generalisation of a different type might be the result.