can anyone explain eigen values and eigen vectors geometrically in a simple manner?

Question

amistre64 · Answer

eugene vectors are vectors that differ only in magnitude

amistre64 · Answer

the values are how we find the vectors, if i recall it correctly

anonymous · Answer

I know a cool example, one sec...

amistre64 · Answer

$$Ax=\lambda x$$
$$Ax-\lambda x=0$$
$$(A-\lambda) x=0$$

anonymous · Answer

http://en.wikipedia.org/wiki/File:Mona_Lisa_eigenvector_grid.png a visual representation of the concept of the eigenvector

unklerhaukus · Answer

$(\textbf A-\textbf I\lambda)x=0$

anonymous · Answer

true, but they said a "geometric" interpretation, so I gave that link...

unklerhaukus · Answer

only take away form the main diagonal , not from every element of  matrix A

amistre64 · Answer

correct, I was implying it which prolly made it rather vague ...

anonymous · Answer

a little bit elaborate guys...

anonymous · Answer

you want elaboration?

amistre64 · Answer

the "how tall you are" marks on the wall while you were growing up can represent a e-vector

anonymous · Answer

In the Mona Lisa pic I linked the shift of the image can be mathematically represented by a linear transformation T(x)=Ax
any vector x=b that is not shifted by the linear transformation or is exactly reversed (in the picture it is the vertical vector) is an eigenvector

anonymous · Answer

ok thanks man

anonymous · Answer

sure thing