IV. Condensation of determinants, being a new and brief method for computing their arithmetical values

Abstract

If it be proposed to solve a set of n simultaneous linear equations, not being all homogeneous, involving n unknowns, or to test their compatibility when all are homogeneous, by the method of determinants, in these, as well as in other cases of common occurrence, it is necessary to compute the arithmetical values of one or more determinants—such, for example, as 1, 3, -2 2, 1, 4 3, 5, -1. Now the only method, so far as I am aware, that has been hitherto employed for such a purpose, is that of multiplying each term of the first row or column by the determinant of its complemental minor, and affecting the products with the signs + and — alternately, the determinants re­quired in the process being, in their turn, broken up in the same manner until determinants are finally arrived at sufficiently small for mental com­putation.

Locations

• Proceedings of the Royal Society of London - View - PDF