Eigenvalue, eigenvector-geometric interpretation in R2

[i]u[/i] is an eigenvector of matrix [i]A[/i], if its image through [i]A[/i] (i.e. [i]A*u[/i]), is collinear with [i]u[/i]. The corresponding eigenvalue -lambda- is the ratio of the (components of the) vectors [i]Au[/i] and [i]u[/i]. Move the vector [i]u[/i] (drag the point [math]P[/math]) till the vectors [i]Au[/i] and [i]u[/i] becomes collinear. Then [i]u[/i] is an eigenvector of matrix [i]A[/i], lambda is the corresponding eigenvalue.

 

kupanpal

 
Resource Type
Activity
Tags
algebra  eigenvalue  eigenvector  vectors 
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
GeoGebra version
4.0
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