### 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 contribution | Utilisation of geometric algebra: compound matrices and the determinant of the sum of two matrices |
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Original language | English |

Pages (from-to) | 273 - 285 |

Number of pages | 13 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 459 (2030) |

DOIs | |

Publication status | Published - Feb 2003 |

### Bibliographical note

Publisher: The Royal Society## Fingerprint Dive into the research topics of 'Utilisation of geometric algebra: compound matrices and the determinant of the sum of two matrices'. Together they form a unique fingerprint.

## Cite this

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