Arrangement of eigenvalues in a Diagonal matrix

[coconut62]

Homework Statement

Is it necessary to arrange the eigenvalues in increasing value order?

As shown in the image attached, if I arrange my eigenvalues -2, -1, 1 diagonally, my D would be
2^8 , 1, 1 diagonally.

However if i arrange it as, say, -1, 1, -2, my D would be different.

Just want to make sure of it, thanks.

 

[Dick]

Homework Statement

Is it necessary to arrange the eigenvalues in increasing value order?

As shown in the image attached, if I arrange my eigenvalues -2, -1, 1 diagonally, my D would be
2^8 , 1, 1 diagonally.

However if i arrange it as, say, -1, 1, -2, my D would be different.

Just want to make sure of it, thanks.

Good work. Yes, there is more than one matrix P that will diagonalize A. You can arrange the eigenvectors in P in a different order and get the eigenvalues in a different order along the diagonal. I don't think anyone order is more correct than another.