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

28 HISTORY OF THE THEORY OF DETERMINANTS

ECHEGARAY, J. (1868): DAYIDOV, A. J. (1868):
"UN ABONNE " (1868).
[Memoria sobre la teoria de las determinantes. Memorias y documentos (Madrid), viii. pp. 244-444.]
[Algebra (in Russian). Moskva.]
[Expose des principes 616mentaires de la theorie des determinants.
Nouv. Annales de Math., (2) vii. pp. 403-413, viii. pp. 97-113.]
The author of the first ' of these is said to have considered his
work little more than a free translation of Truli's. The third is
of no moment.
HESSE, 0. (1868).
[Ein Determinantensatz. Grelle's Journ., lxix. pp. 319-322; or
Werke, pp. 557-560.]
The theorem in question is, in iesse's notation, that if
3B 'aB
A ~ ' a22~ a,,, B = aDA/1aapq, P = DB a, -DB "
'aa,,p DaA, 2
K/
then
DB aB ___
'A - + P B - ( qB Z _ a a
'aaae?,(t,P '~Ipq3aa,,DKX aKqapx
It is brought forward and established mainly for the sake of the
case where B = 0, the deduction being that A is then expressible
as the product of two factors of the form
(X1(a,,+ a2q +... + Xnanq)(,xlaii, ~ a42ctP2 +.. + -UanC);
or, taking without loss of generality p = q = n and = n n- 1,
that
DBe __ aB DB
- A = a1, + - qLn + +. +
fB 'aDB DB
aa,,-1+ aa n1,2 Ja,?
*Neither this nor the second have I been fortunate enough to see.