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# Diagonalisation and Eigenvectors watch

1. Hey,

When finding a matrix P such that D=P-1ATP, where D is a diagonal matrix.

I found the eigenvalues of AT and the corresponding eigenvectors. When forming the matrix P, does it matter which order I place the eigenvectors in as the columns?

I found a diagonal matrix D, which was different than the one given in the solutions. Will this matter? Or will any diagonal matrix formed with the correct eigenvectors be fine?

Thanks

Jamie
2. It does not matter, as long as your eigenvalues and corresponding eigenvectors are correct (and of course the final matrix D is diagonal).
3. (Original post by Math12345)
It does not matter, as long as your eigenvalues and corresponding eigenvectors are correct (and of course the final matrix D is diagonal).
Thank you
4. (Original post by Math12345)
It does not matter, as long as your eigenvalues and corresponding eigenvectors are correct (and of course the final matrix D is diagonal).
Correct me if I'm wrong but I thought the corresponding eigenvectors have to be in the same column as the eigenvalues in D.

So if D=

2 0
0 -3

Then the eigenvector corresponding to the eigenvalue 2 would have to be the first column of P and likewise with -3.
5. (Original post by poorform)
Correct me if I'm wrong but I thought the corresponding eigenvectors have to be in the same column as the eigenvalues in D.

So if D=

2 0
0 -3

Then the eigenvector corresponding to the eigenvalue 2 would have to be the first column of P and likewise with -3.
Yes that is right. Sorry if I didn't mention it above.

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Updated: April 19, 2016
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