Polynomial matrices, splitting subspaces and Krylov subspaces over finite fields
نویسندگان
چکیده
Let T be a linear operator on vector space V of dimension n over Fq. For any divisor m n, an m-dimensional subspace W is T-splitting ifV=W⊕TW⊕⋯⊕Td−1W, where d=n/m. σ(m,d;T) denote the number subspaces. Determining for arbitrary open problem that closely related to another important Krylov spaces. We discuss this connection and give explicit formulae in case invariant factors satisfy certain degree conditions. A with enumeration polynomial matrices also discussed.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2022
ISSN: ['1090-2465', '1071-5797']
DOI: https://doi.org/10.1016/j.ffa.2022.102081