Repeated eigenvectors vs Complex eigenvectors

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Let's consider a generic 3x3 matrix. We study eigenvalues and eigenvectors in order to know what's the general behavior of the transformation the matrix produces.



In the case of a 3x3 matrix with only 1 repeated eigenvalue (repeated 3 times) we know that there is only 1 direction that get only stretched by the transformation the matrix produce.
In the case of a 3x3 matrix 1 with real eigenvalue and 2 complex conjugates eigenvalues we know that there is only 1 direction that get only stretched, If we feed the matrix with real vectors.



So, the behaviour of these 2 matrice in respect of real vectors is qualitatively the same. Is correct ?
If yes, what is the difference, which at the moment i'm not able to grab, between these two types of matrices?




linear-algebra geometry




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  • What about the matrix $2I$?
    – Bernard
    Jul 22 at 16:01














up vote
-1
down vote

favorite












Let's consider a generic 3x3 matrix. We study eigenvalues and eigenvectors in order to know what's the general behavior of the transformation the matrix produces.



In the case of a 3x3 matrix with only 1 repeated eigenvalue (repeated 3 times) we know that there is only 1 direction that get only stretched by the transformation the matrix produce.
In the case of a 3x3 matrix 1 with real eigenvalue and 2 complex conjugates eigenvalues we know that there is only 1 direction that get only stretched, If we feed the matrix with real vectors.



So, the behaviour of these 2 matrice in respect of real vectors is qualitatively the same. Is correct ?
If yes, what is the difference, which at the moment i'm not able to grab, between these two types of matrices?




linear-algebra geometry




share|cite|improve this question





















  • What about the matrix $2I$?
    – Bernard
    Jul 22 at 16:01












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











Let's consider a generic 3x3 matrix. We study eigenvalues and eigenvectors in order to know what's the general behavior of the transformation the matrix produces.



In the case of a 3x3 matrix with only 1 repeated eigenvalue (repeated 3 times) we know that there is only 1 direction that get only stretched by the transformation the matrix produce.
In the case of a 3x3 matrix 1 with real eigenvalue and 2 complex conjugates eigenvalues we know that there is only 1 direction that get only stretched, If we feed the matrix with real vectors.



So, the behaviour of these 2 matrice in respect of real vectors is qualitatively the same. Is correct ?
If yes, what is the difference, which at the moment i'm not able to grab, between these two types of matrices?




linear-algebra geometry




share|cite|improve this question













Let's consider a generic 3x3 matrix. We study eigenvalues and eigenvectors in order to know what's the general behavior of the transformation the matrix produces.



In the case of a 3x3 matrix with only 1 repeated eigenvalue (repeated 3 times) we know that there is only 1 direction that get only stretched by the transformation the matrix produce.
In the case of a 3x3 matrix 1 with real eigenvalue and 2 complex conjugates eigenvalues we know that there is only 1 direction that get only stretched, If we feed the matrix with real vectors.



So, the behaviour of these 2 matrice in respect of real vectors is qualitatively the same. Is correct ?
If yes, what is the difference, which at the moment i'm not able to grab, between these two types of matrices?





linear-algebra geometry





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 22 at 16:00









Bernard

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asked Jul 22 at 15:53









Koinos

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  • What about the matrix $2I$?
    – Bernard
    Jul 22 at 16:01
















  • What about the matrix $2I$?
    – Bernard
    Jul 22 at 16:01















What about the matrix $2I$?
– Bernard
Jul 22 at 16:01




What about the matrix $2I$?
– Bernard
Jul 22 at 16:01















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