This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 Excerpt: ...pth class, which is formed by keeping the first suffixes unaltered, and writing for each set of the other suffixes all possible permutations of 1, 2... re. To each term so obtained we give the sign corresponding to the sum of the number of inversions in the p--1 sets of variable suffixes. The whole number of terms is ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 Excerpt: ...pth class, which is formed by keeping the first suffixes unaltered, and writing for each set of the other suffixes all possible permutations of 1, 2... re. To each term so obtained we give the sign corresponding to the sum of the number of inversions in the p--1 sets of variable suffixes. The whole number of terms is re!-1. 11. The determinant of the joth class can be represented as a product of linear factors of the elements which lie in the same paralleloscheme of p--1 dimensions. If &l, 3 ei ei, e2... en %. Vi Vn be p--1 sets of alternate units; it is plain from reasoning similar to that in Art. 3, that the function (where the sum is formed by giving to each of the suffixes j, k...l all values from 1 to n, and then forming the product of such sums for the values 1, 2... n of i) is a determinant of the pth class and nth order, such as we have defined in Art. 10. 12. This definition is strictly analogous to those for determinants of the second and third class. A determinant of the second class is the product of linear functions of the elements of a row, one of the third class the product of n factors linear in the elements of a stratum. Here the determinant of the th class is the product of n factors linear in the elements of a paralleloscheme of p--1 dimensions. 13. It is clear that by the interchange of any two suffixes, except the first, the determinant changes sign. Also since the factors of the determinant can be written as linear expressions of each of the p--1 sets of alternate units, it follows that by the interchange of two first suffixes the determinant undergoes p--1 independent changes of sign. Thus the determinant remains unaltered or changes sign according as its class is odd or even. 14. We have kept the first suffixes in their natural o...
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Add this copy of The Theory of Determinants and Their Applications to cart. $27.93, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1904 by Cornell University Library.
Add this copy of The Theory of Determinants and Their Applications to cart. $54.34, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 1904 by Cornell University Library.
