Computing the cardinality of the lattice of characteristic subspaces

[EN] We obtain the cardinality of the lattice of characteristic sub-spaces of a nilpotent Jordan matrix when the underlying field is GF(2), the only field where the lattices of characteristic and hyperinvariant subspaces can be different. If the charac-teristic polynomial of the matrix splits in the field, the general case can be reduced to the nilpotent Jordan case. Results are complex and highly combinatorial, and include the design of an algorithm.The second author is partially supported by grant MTM2015-65361-P MINECO/FEDER, UE. The third author is partially supported by grants MTM2013-40960-P MINECO and MTM2015-68805-REDT.Mingueza, D.; Montoro, M.; Roca Martinez, A. (2017). Computing the cardinality of the lattice of characteristic subspaces. Linear Algebra and its Applications. 514:82-104. https://doi.org/10.1016/j.laa.2016.10.031S8210451