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VI.—Note on the m-line Determinants whose Elements are (m−1)-line Minors of an m-by-(m + k) Array
Published online by Cambridge University Press: 15 September 2014
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(1) If note be taken that, when k in the title is 0, there is only one such determinant, namely the adjugate, it will be seen that what we are about to consider is a family of compound determinants which includes the adjugate as a very special case. Such determinants have not altogether escaped study, but until recently the attention paid to them has been incidental and fragmentary.
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page 52 note * It will be found interesting to compare these equalities with corresponding results arrived at in a paper recently published by Mr W. L. Ferrar in the Proc. London Math. Soc., xxii, pp. 29–36. The work of comparison will be lightened if it be noted that the elements of the compound determinants in question are there denoted by the numbers of the rows and columns omitted from the array in order to obtain the element: for example the element |bαcβdγ| is in effect denoted by (α ; δ, ε) and in reality by Aδ, ε.
page 54 note * Beiträge zur Theorie der Determinanten, p. 64.
page 54 note † On p. 23 of vol. iii of my History I drew attention to the fact that the Beiträge had been as good as buried at its birth. “His work is not even mentioned by any of the German textbooks that give bibliographical references, namely, Baltzer's editions of 1870, 1875, 1881, and Günther's of 1875, 1877.” To these I may now add Leitzmann's of 1900 and Kowalewski's of 1909.
page 54 note ‡ Messenger of Math., xxxv, pp. 118–122.
page 54 note § Proc. Edinburgh Math. Soc., xxxvi, pp. 107–115.
page 55 note * For a still wider theorem than mine of 1905 see a paper by Prof.Turnbull, H. W. in Trans. Cambridge Philos. Soc., xxi (1909, pp. 197–240.Google Scholar