Namespaces
Variants
Actions

Difference between revisions of "Reducible representation"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(details)
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
A [[Linear representation|linear representation]] on a vector space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080410/r0804101.png" /> over a field <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080410/r0804102.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080410/r0804103.png" /> contains a proper non-zero [[Invariant subspace|invariant subspace]].
+
{{TEX|done}}
 
+
A [[Linear representation|linear representation]] on a vector space $V$ over a field $k$ such that $V$ contains a proper non-zero [[invariant subspace]].
 
 
 
 
====Comments====
 
 
 
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  C.W. Curtis,   I. Reiner,   "Methods of representation theory" , '''1–2''' , Wiley (Interscience) (1981–1987)</TD></TR></table>
+
* {{Ref|a1}} C.W. Curtis, I. Reiner, "Methods of representation theory", '''1–2''', Wiley (Interscience) (1981–1987)

Latest revision as of 13:50, 8 April 2023

A linear representation on a vector space $V$ over a field $k$ such that $V$ contains a proper non-zero invariant subspace.

References

  • [a1] C.W. Curtis, I. Reiner, "Methods of representation theory", 1–2, Wiley (Interscience) (1981–1987)
How to Cite This Entry:
Reducible representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reducible_representation&oldid=12830
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article