Utilisation of geometric algebra: compound matrices and the determinant of the sum of two matrices

U Prells, MI Friswell, SD Garvey

Research output: Contribution to journalArticle (Academic Journal)

14 Citations (Scopus)

Abstract

In this paper we demonstrate the capabilities of geometric algebra by the derivation of a formula for the determinant of the sum of two matrices in which both matrices are separated in the sense that the resulting expression consists of a sum of traces of products of their compound matrices. For the derivation we introduce a vector of Grassmann elements associated with an arbitrary square matrix, we recall the concept of compound matrices and summarise some of their properties. This paper introduces a new derivation and interpretation of the relationship between p-forms and the pth compound matrix, and demonstrates the utilisation of geometric algebra, which has the potential to be applied to a wide range of problems.
Translated title of the contributionUtilisation of geometric algebra: compound matrices and the determinant of the sum of two matrices
Original languageEnglish
Pages (from-to)273 - 285
Number of pages13
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume459 (2030)
DOIs
Publication statusPublished - Feb 2003

Bibliographical note

Publisher: The Royal Society

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