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

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.

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Link to paper using doi:10.1098/rspa.2002.1040

Proceedings of the Royal Society of London, Series A

The Royal Society of London