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| Title of object: |
invariant subspace |
| Canonical Name: |
InvariantSubspace |
| Type: |
Definition |
| Created on: |
2002-02-15 00:51:19 |
| Modified on: |
2005-08-02 22:50:53 |
| Classification: |
msc:15-00 |
Preamble:
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\newtheorem{proposition}{Proposition} |
Content:
Let $T: V\rightarrow V$ be a linear transformation of a vector space $V$. A subspace $U\subset V$ is
called an {\em invariant subspace} of $T$ if
$$T(U)\subset U$$
If $U$ is an invariant subspace, then the restriction of $T$ to $U$ defines a well defined linear transformation
of $U$. |
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