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Published online by Cambridge University Press: 06 July 2012
(1) There being n2 independent variables in a general n-line determinant, the Hessian of the determinant with respect to the said variables must be a determinant with n2 lines: and as a general n-line determinant has all its terms linear in the elements involved, it follows that each element of the Hessian being a second differential-quotient cannot be of a higher degree in the variables than the (n − 2)th, and that consequently the degree of the Hessian itself cannot exceed n2(n − 2). The object of the present short paper is to show that this degree is attained by the n(n − 2)th power of the given determinant being a factor of the Hessian.
page 206 note * Note, too, that the determinant of every matrix vanished, being, in the case exemplified, the square of the vanishing Pfaffian
