Diagonalise,

=

That is find matrices P and D, where D is diagonal such that

P-1 AP = D

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- May 17th 2008, 09:08 PMpearlycDiagonalise Symmetric Matrix.
Diagonalise,

=

That is find matrices P and D, where D is diagonal such that

P-1 AP = D - May 17th 2008, 09:15 PMIsomorphism

**Hint1:**D is the matrix with eigenvalues in the diagonal.

**Hint2:**P is the 3 x 3 matrix formed by writing the corresponding eigenvectors as columns.

**Reference:**Diagonalizable matrix - Wikipedia, the free encyclopedia - May 17th 2008, 09:47 PMpearlyc
Yeah, I am having slight difficulties finding the eigenvectors.

Tried doing row reducing or 3 x 3 matrix determinant way, still can't really get the eigenvalues. - May 17th 2008, 10:15 PMIsomorphism
- May 18th 2008, 06:53 AMpearlyc
Oh really? You can't diagonalise if it's det. is 0?

I am really confused at the moment because this is an assignment question and it is directing us to diagonalise it! Does sound like it's really diagonalisable though.

Sighhh. - May 18th 2008, 07:15 AMIsomorphism
- May 18th 2008, 07:20 AMpearlyc
I got 0 and + - root 6, I am not sure if this is correct or not!

- May 18th 2008, 07:24 AMMoo
- May 18th 2008, 07:26 AMpearlyc
Okay, the eigenvectors are gonna be quite confusing to be done right!

- May 18th 2008, 07:30 AMIsomorphism
- May 18th 2008, 07:32 AMMoo
Hm, for for example :

The third one will just yield the first one (Wink)

From the first equation, we get :

Substituting in the second one :

-->

Taking , and

The eigenvector associated to is - May 18th 2008, 07:33 AMpearlyc
Can I find the eigenvectors by using the method where we do a cross product from selecting two columns from the A-lamda.I?