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

643 HISTORY OF THE THEORY OF DETEiMINANTS

whose m-line minors do not all vanish and a set of m columns with the
same property, then the m-line minor common to the two sets cannot
possibly vanish. What follows on this mainly concerns skew determinants, and is therefore dealt with elsewhere.
HOZA, F. (1876).
[Ueber das Multiplicationstheorem zweier Determinanten n-ten
Grades. Archiv d. Math. u. Phys., lix. pp. 403-406; or, in
Czech, Casopis pro pestovdni math. a fys., vi. pp. 87-89.]
The procedure is that adopted by Janni (1873), and is not more
effectively carried out.
HOZA, F. (1876).
[Ueber Unterdeterminanten einer adjungirten Determinante.
Archiv d. Math. u. Phys., lix. pp. 401-403.]
This is simply the ordinary proof (Cayley's, 1843) with fuller
details and explanations for the benefit of beginners.
JOHNSON, W. W. (1876): DICK, G. R. (1878):
TANNER, H. W. L. (1879).
[On the determination of the sign of any determinant. Messenger
of Math., vii. p. 59.]
[On the sign of any term of a determinant. Educ. Times, xxxi.
p. 161; or Math. from Educ. Times, xxix. pp. 99-100.]
[On the sign of any term of a determinant. Messenger of Math.,
ix. pp. 51-52.]
Johnson's rule and Dick's are both to be found in Cauchy (1812),
the one being that in which circular substitutions are counted, and
the other that connected with the difference-product.
Tanner's is of considerably more interest. If the determinant
be a15 1, and the sign of al3a21a32a45a54 be wanted, he writes the
row-subscripts of the determinant and under them the columnsubscripts, both in their natural order, thus
1 2 3 4 5
1 2 3 4 5;