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

CHAPTER XI.

ORTIOGONANTS, FROM 1855 TO 1879.
FROM the study of the subject of linear transformation there arise
two quite distinct matters for consideration in the theory of determinants; namely, first, the properties of a special form of determinant known as an Orthogonant, and, second, the character of
the roots of Lagrange's determinantal equation. At first the two
matters were interlocked: in the present volume this is no longer
quite the case, the papers being without much difficulty separable
into the two relevant groups. As, however, the subject of the second
group is still on the whole viewed in connection with orthogonal
transformation, the separation has not been made. The reader,
therefore, who is interested in what came soon to be known as the
subject of the Latent Roots of a Determinant must still turn to
Orthogonants.
We have only further to remark that the first of the papers
belongs to the twenty-year period immediately preceding, and that
between the two periods there is little difference to be noted in the
matter of fruitfulness.
CAUCHY, A. (1855).
[Sur le denombrement des racines qui, dans une equation algebrique
ou transcendante, satisfont a des conditions donnees. Comptes
Rendus... Acad. des Sci. (Paris), xl. pp. 1329-1335; or
(Euvres completes, (1) xii. pp. 293-299.]
What concerns us here is the one or two corollaries to the second
of three theorems on the subject matter of the title, the main corollary being that the equation