The number of invariant subspaces under a linear operator on finite vector spaces | Zendy

Harald Fripertinger | Zendy

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The number of invariant subspaces under a linear operator on finite vector spaces

Author(s) -

Harald Fripertinger

Publication year - 2011

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2011.5.407

Subject(s) - linear subspace , mathematics , finite field , enumeration , linear operators , invariant (physics) , vector space , linear map , combinatorics , operator (biology) , continuous linear operator , discrete mathematics , pure mathematics , mathematical analysis , mathematical physics , biochemistry , chemistry , repressor , gene , transcription factor , bounded function

Let $V$ be an $n$-dimensional vector space over the finite field $\mathbb F$q and $T$ a linear operator on $V$. For each $k\in\{1,\ldots,n\}$ we determine the number of $k$-dimensional $T$-invariant subspaces of $V$. Finally, this method is applied for the enumeration of all monomially nonisometric linear $(n,k)$-codes over $\mathbb F$q.

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