invariant subspace
Let be a linear transformation of a vector space . A subspace
is
called a -invariant subspace
if for all .
If is an invariant subspace, then the restriction of to
gives a well defined linear transformation of . Furthermore,
suppose that is -dimensional and that is a
basis of with the first vectors giving a basis of . Then,
the representing matrix of the transformation
relative to this
basis takes the form
where is an matrix representing the restriction transformation relative to the basis .
Title | invariant subspace |
---|---|
Canonical name | InvariantSubspace |
Date of creation | 2013-03-22 12:19:55 |
Last modified on | 2013-03-22 12:19:55 |
Owner | rmilson (146) |
Last modified by | rmilson (146) |
Numerical id | 9 |
Author | rmilson (146) |
Entry type | Definition |
Classification | msc 15-00 |
Related topic | LinearTransformation |
Related topic | Invariant![]() |