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

42 HISTORY OF THE THEORY OF DETERMINANTS

Incidentally to this proof it is shown that
~th11+x h~12... x'l +1 "A 412..
P=A A21 j~h22 +... Q =B 1C,21 \JC22 + A
n
where
A1 Ari~!b
and /al=BI- a, +Br2a. + B1r,,
B ~'+B +B
and where therefore
B k =A
A' B
Putting f(u) for P when A = 1, and multiplying f (u) by the
expression which the theorem gives for f ( —,A) Siacci readily obtains
f(1x) *f-,t~) AB h1l - ICI2hn- cd2
2n 2n
hn- ZknIIA... hnn - Jf~nk2
where the It's and k's are such that
hylk1, + hr2 -H..- hrn lknr 1,
hrlkis~ H hr2 k98 -I. 12I hj21kils 0.
The remaining portions of the two papers are occupied with
deductions, some of which fall under Orthogonants and one under
iRecurrents.
STUDNICKA,5 F. J. (1872): WALKER, J. J. (1872).
[Novy' du'kaz pouc'ky o pomerech mezi ptivodnimlf a pr~edruz'enymi~
V
determinanty a subdeterminanty. Casopis pro p'Cstovt'nimath.
a phys., i. pp. 6-10.]
[Question 3690. Educ. Times, xxiv. p. 296; or Math. from Educ.
Times, xvii. pp. 110-111.]
Studnic'ka's so-called proof of Jacobi's theorem regarding a
minor of the adjugate is only suggestive of the truth: and Walker's
identity is that which began to appear with Monge in 1809, and which
came later to be known as the 'extensional' of.I ab2 IIc~d, I - Ijac2[I bd2J + Ia~d2IjjbC2~ I 0.