Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-29T01:48:54.710Z Has data issue: false hasContentIssue false

Determinant Expansions

Published online by Cambridge University Press:  03 November 2016

Extract

A Set of numbers aij (called elements) arranged in a rectangular array of m rows and n columns constitutes a matrix of orders m × n. For example, of the arrays

the first is a matrix of two rows and three columns, i.e. of orders 2 × 3, the second is a square matrix of orders 3 × 3.

From a square matrix of orders n × n we can form a determinant of order n. Thus from the above square matrix we can form the determinant of order 3

Type
Research Article
Copyright
Copyright © Mathematical Association 1941 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

page no 132 note * Rice, L. H. (American Jour. of Math. 42, p. 237 (1920))CrossRefGoogle Scholar. This remarkable and general theorem appears to have been overlooked by writers on determinants.

page no 134 note * Albeggiani, M. (Giornale di Mat., 13, p. 1 (1874))Google Scholar. The proof which follows is due to Rice, loc. cit.