!!! Overview [1] [2]
[{$pagename}] or characteristic vector of a [linear transformation] is a __non-zero__ [vector] that only changes by an overall scale when that [linear transformation] is applied to it. 

More formally, if T is a [linear transformation] from a [vector] space V over a field F into itself and v is a [vector] in V that is not the zero vector, then v is an [{$pagename}] of T if T(v) is a scalar multiple of v. This condition can be written as the equation
%%prettify 
{{{
T(V) =λv
}}} 
/%


Below [Matrix] A acts by stretching the [vector] x, not changing its direction, so x is an [{$pagename}] of A.


[https://upload.wikimedia.org/wikipedia/commons/thumb/5/58/Eigenvalue_equation.svg/500px-Eigenvalue_equation.svg.png]




!! More Information
There might be more information for this subject on one of the following:
[{ReferringPagesPlugin before='*' after='\n' }]
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* [#1] - [Eigenvalues_and_eigenvectors|Wikipedia:Eigenvalues_and_eigenvectors|target='_blank'] - based on information obtained 2017-12-28- 
* [#2] - [Eigenvectors and Eigenvalues|http://setosa.io/ev/eigenvectors-and-eigenvalues/|target='_blank'] - based on information obtained 2017-12-28-