1917/02/01 by E. T. Whittaker · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Mathematics and Applications #Advanced Topology and Set Theory
paper · pdf · doi:10.1017/s001309150003529x
openalex publication_date 1917/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The present paper is concerned with determinants whose elements are themselves determinants. The best-known determinants of this kind are those whose elements are minors of a given determinant; these are called the “adjugate” and the “compounds” of the given determinant. Determinants whose elements are themselves determinants also occur frequently in Muir's theory of Extensionals. The determinants considered in the present paper are of a somewhat more general type than adjugates, compounds, and extensionals; the principal result obtained is “Theorem A” (at the end of § 2), which relates to determinants whose elements are formed from any number of arrays. It is shown in § 3 that many other formulae, both new and old, may be obtained by specialising the arrays in “Theorem A.”