PCA linear algebra problem (eigenvectors)?

koolkid892

I have done everything thus far successfully but for some reason I can just not get the eigenvectors correct. The matrix that im trying to find eigenvectors for is:

( 2.45 7.35 -1.75 1.75 )

( 7.35 22.05 -5.25 5.25 )

( -1.75 -5.25 1.25 -1.25 )

( 1.75 5.25 -1.25 1.25 )

I have found the eigenvalues to be 0, 0, 0 and 27

I found the eigenvector for 27 successfully, but the 0's are being a pain.

I keep getting: The correct answers (after normalized) are:

(-3) (5/7) (-5/7) (.846) (.004) ( 0 )

( 1) ( 0 ) ( 0 ) (-.401) (.320) ( 0 )

( 0) ( 1 ) ( 0 ) (-.215) (-.670) (.707)

( 0) , ( 0 ), and ( 1 ). (.215) , (.670) and (.707)

Please tell me where I am going wrong.

I have used a multitude of calculators and they all say something different. One even said my answers were right.

Update:

I hate this formatting. Please read my eigenvectors as matricies with 4 rows and 1 column, so that

(-3)

( 1)

( 0)

( 0)

is an eigenvector

ted-s

your eigenvectors are fine for eigenvalue of 0..the 1st could also be < -3 , 1 , 1 , 1 > ;

on my TI 85 one of the vectors is { 4 dec. } < 0.2606 , -0.2919 , 0.0695 , 0.9305 > ;

remember that if W is an eigenvector then so is [a W] , for any a ╪ 0 ;

and if you are worried about the 'normalization ' then remember that

if w1 and w2 are eigenvectors the so is [ a w1 + b w2 ] = w3 and

normalized w1 ╪ normalized w3