Utilisation of Geometric Algebra: Compound Matrices and the Determinant of the Sum of two Matrices
U Prells, MI Friswell (University of Wales Swansea) & SD Garvey (University of Nottingham)
Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 459, No. 2030, February 2003, pp. 273-285
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.
This material has been published in the Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 459, No. 2030, February 2003, pp. 273-285, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by The Royal Society. This material may not be copied or reposted without explicit permission.
Link to paper using doi:10.1098/rspa.2002.1040
Proceedings of the Royal Society of London, Series A
The Royal Society of London