The theory of determinants in the historical order of development, by Sir Thomas Muir.

478 HISTORY OF THE THEORY OF DETERMINANTS

The proposition appears not to have been established. It was
probably brought forward on seeing Scott's use of the functions
in connection with alternants (see chap. v.). Muir's so-called
solution is really the statement of a proposition to be substituted
for Hammond's.
HUNYADY, E. v. (1866).
[Ueber ein Product zweier Determinanten. Zeitschrift f. Math. u,
Phys., xi. pp. 359-360.]
The interest of this is strictly geometrical.
CALDARERA, F. (1866).
[Dei determinanti a matrice magica. Giornale di sci. nat. ed econ.
(Palermo), i. pp. 173-196.]
Evaluations such as
x. -1 1
1 x -I 1
1. x —1. - (x-1)(-x+1)
1 -1 x 1.1 -. x
are made with great fullness of detail, the centrosymmetry being
unobserved.
SYLVESTER, J. J. (1867).
[Thoughts on inverse orthogonal matrices, simultaneous signsuccessions,.... Philos. Magazine, xxxiv. pp. 461-475; or
Collected Math. Papers, ii. pp. 615-628.]
A determinant matrix is said by Sylvester to be 'inversely
orthogonal' when its elements are inversely proportional to the
corresponding elements of the adjugate matrix. This is the same
as to say that the product of any element by its cofactor in the
determinant is constant, and therefore equal to 1/n of the value of
the determinant when the order is n. The name properly implies
contrast with an orthogonant, as the elements of the latter are
directly proportional to the elements of its adjugate.