Tropical compound matrix identities
Commutative Algebra
2019-12-30 v2 Combinatorics
Abstract
We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and~, all of which have implications on the eigenvalues of the corresponding matrices. A tropical Sylvester-Franke identity is provided as well.
Cite
@article{arxiv.1702.00980,
title = {Tropical compound matrix identities},
author = {Marianne Akian and Stephane Gaubert and Adi Niv},
journal= {arXiv preprint arXiv:1702.00980},
year = {2019}
}
Comments
The first two authors have been partially supported by the PGMO Program of FMJH and EDF, and by the MALTHY Project of the ANR Program. This work was performed when the third author was with INRIA Saclay--\^Ile-de-France and CMAP, Ecole polytechnique, and it was supported by the French Chateaubriand grant and INRIA postdoctoral fellowship