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 contribution||Utilisation of geometric algebra: compound matrices and the determinant of the sum of two matrices|
|Pages (from-to)||273 - 285|
|Number of pages||13|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - Feb 2003|
Bibliographical notePublisher: The Royal Society
Prells, U., Friswell, MI., & Garvey, SD. (2003). Utilisation of geometric algebra: compound matrices and the determinant of the sum of two matrices. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 459 (2030), 273 - 285. https://doi.org/10.1098/rspa.2002.1040