Tropical compound matrix identities
arXiv:1702.00980 · doi:10.1016/j.laa.2018.04.006
Abstract
We prove identities on compound matrices in extended tropical semirings. Such identities include analogues to properties of conjugate matrices, powers of matrices and~$\adj(A)\det(A)^{ -1}$, all of which have implications on the eigenvalues of the corresponding matrices. A tropical Sylvester-Franke identity is provided as well.
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--Île-de-France and CMAP, Ecole polytechnique, and it was supported by the French Chateaubriand grant and INRIA postdoctoral fellowship