Eigenvalues and Eigenvectors of Matrices in Idempotent Algebra
Nikolai Krivulin · 2006
Abstract-The eigenvalue problem for the mattix of a generalized linear operator is considered. In the case of irreducible mattices, the problem is reduced to the analysis of an idempotent analogue of the charactetistic polynomial of the mattix. The eigenvectors are obtained as solutions to a homogeneous equation. The results are then extended to cover the case of an arbitrary mattix. It is shown how to build a basis of the eigensubspace of a mattix. In conclusion, an inequality for matlix powers and eigenvalues is presented, and some extremal properties of eigenvalues are considered. 1.