Linear Algebra Unique Factorization

[sportsfan1292]

Homework Statement

Assume that the matrix A is diagonalizable : A=PDP^-1, where D is the diagonal matrix of eigenvalues. Show that this factorization is not always unique

Homework Equations

The Attempt at a Solution

I have a couple of theories. The first being that since the matrix D can be reordered in any way as long as the eigenvalues are on the diagonal.
The second is that A=P^-1CP when C is the non diagonalized matrix.

 

[Mark44]

I like your first theory. The order of the eigenvalues on the main diagonal of D depends on the order of placement of eigenvectors in P.