Admissibility 2003-12-02 04:51:39 2004-03-15 08:30:32 Definition % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Let $k$ be a field, $V$ a vector space over $k$, and $T\colon V\to V$ a linear operator. We say that a subspace $W$ of $V$ is $T$-\emph{admissible} if \begin{enumerate} \item $W$ is a $T$ - invariant subspace; \item If $f \in k[X]$ (See the polynomial ring definition) and $f(T)x \in W$, there is a vector $y \in W$ such that $f(T)x=f(T)y$. \end{enumerate}