Signs in objective linear algebra, exemplified with exterior powers and determinants

/ Authors

/ Abstract

We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an objective treatment of exterior powers and determinants.

Signs in objective linear algebra, exemplified with exterior powers and determinants

/ Authors

Joachim Kock, Jesper M. Møller

/ Abstract

We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an objective treatment of exterior powers and determinants.