Enumerating Invariant Subspaces of ${\mathbb R}^n$

Details Enumerating Invariant Subspaces of ${\mathbb R}^n$ Enumerating Invariant Subspaces of ${\mathbb R}^n$

2012-01-13

arxiv.org/abs/1201.2958v1

Mathematics

Rings and Algebras

Scientific paper

In this article, we develop an algorithm to calculate the set of all integers
$m$ for which there exists a linear operator $T$ on ${\mathbb R}^n$ such that
${\mathbb R}^n$ has exactly $m$ $T$-invariant subspaces. A brief discussion is
included as how these methods might be extended to vector spaces over arbitrary
fields.

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