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3
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Given a subdomain of GL(n), when is the map from matrices to their matrices of eigenvectors ...
Whatever the way you define your map, you cannot expect a diffeomorphism for dimension reasons. The simple fact that you can rescale your eigenvectors makes you lose some dimensions (at least n). In a …
1
vote
Relating eigenvectors of two self-adjoints operators
So your question seems to be : what is the connection between the eigenvectors of $A_1=Dbb^TD^T$ and $A_2=Db_\perp b_\perp^TD^T$ ?
Well it's easy to find these eigenvectors. First case : $Db,Db_\perp …