- #1
DryRun
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Homework Statement
For a 3x3 matrix A, i know the eigenvalues and their corresponding 3 eigenvectors.
Define a matrix P such that ##PAP^{-1}## is a diagonal matrix.
Homework Equations
Similarity transformation formula: ##D=P^{-1}AP## where D is the diagonal matrix containing the eigenvalues as its trace elements.
The Attempt at a Solution
The 3 eigenvectors form a 3x3 matrix P.
The problem is that I've learned the formula to be: ##D=P^{-1}AP##
But what is being asked here is: ##PAP^{-1}##
I've re-arranged the matrix, ##D=P^{-1}AP##, into: ##PDP^{-1}=IAI## which gives ##PDP^{-1}=A## but i have no idea what to do next.