Proof that the Trace of a Matrix is the sum of its Eigenvalues for non diagonalizable matrices












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Proof that the Trace of a Matrix is the sum of its Eigenvalues
How does the proof given by Prof.Ted Shriffin for the above question work when the matrix is non diagonalizable?
In the video which has the same proof https://www.youtube.com/watch?v=OLl_reBXY-g&list=PLlXfTHzgMRUIqYrutsFXCOmiqKUgOgGJ5&index=20 Prof.Pavel says that we have to deal the proof in a more subtle way when the matrix is non diagonalizable.










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  • $begingroup$
    I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
    $endgroup$
    – Eric
    Dec 2 '18 at 17:15






  • 1




    $begingroup$
    Why do you think the proof by Ted Shifrin assumes that the matrix is not defective? It seems to me that it works as written for all matrices (with the helpful explanation in the comment by MEB).
    $endgroup$
    – Alex Kruckman
    Dec 2 '18 at 17:16


















0












$begingroup$


Proof that the Trace of a Matrix is the sum of its Eigenvalues
How does the proof given by Prof.Ted Shriffin for the above question work when the matrix is non diagonalizable?
In the video which has the same proof https://www.youtube.com/watch?v=OLl_reBXY-g&list=PLlXfTHzgMRUIqYrutsFXCOmiqKUgOgGJ5&index=20 Prof.Pavel says that we have to deal the proof in a more subtle way when the matrix is non diagonalizable.










share|cite|improve this question











$endgroup$












  • $begingroup$
    I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
    $endgroup$
    – Eric
    Dec 2 '18 at 17:15






  • 1




    $begingroup$
    Why do you think the proof by Ted Shifrin assumes that the matrix is not defective? It seems to me that it works as written for all matrices (with the helpful explanation in the comment by MEB).
    $endgroup$
    – Alex Kruckman
    Dec 2 '18 at 17:16
















0












0








0





$begingroup$


Proof that the Trace of a Matrix is the sum of its Eigenvalues
How does the proof given by Prof.Ted Shriffin for the above question work when the matrix is non diagonalizable?
In the video which has the same proof https://www.youtube.com/watch?v=OLl_reBXY-g&list=PLlXfTHzgMRUIqYrutsFXCOmiqKUgOgGJ5&index=20 Prof.Pavel says that we have to deal the proof in a more subtle way when the matrix is non diagonalizable.










share|cite|improve this question











$endgroup$




Proof that the Trace of a Matrix is the sum of its Eigenvalues
How does the proof given by Prof.Ted Shriffin for the above question work when the matrix is non diagonalizable?
In the video which has the same proof https://www.youtube.com/watch?v=OLl_reBXY-g&list=PLlXfTHzgMRUIqYrutsFXCOmiqKUgOgGJ5&index=20 Prof.Pavel says that we have to deal the proof in a more subtle way when the matrix is non diagonalizable.







linear-algebra matrices eigenvalues-eigenvectors






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share|cite|improve this question













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edited Dec 3 '18 at 5:44







Akhil

















asked Dec 2 '18 at 16:37









AkhilAkhil

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  • $begingroup$
    I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
    $endgroup$
    – Eric
    Dec 2 '18 at 17:15






  • 1




    $begingroup$
    Why do you think the proof by Ted Shifrin assumes that the matrix is not defective? It seems to me that it works as written for all matrices (with the helpful explanation in the comment by MEB).
    $endgroup$
    – Alex Kruckman
    Dec 2 '18 at 17:16




















  • $begingroup$
    I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
    $endgroup$
    – Eric
    Dec 2 '18 at 17:15






  • 1




    $begingroup$
    Why do you think the proof by Ted Shifrin assumes that the matrix is not defective? It seems to me that it works as written for all matrices (with the helpful explanation in the comment by MEB).
    $endgroup$
    – Alex Kruckman
    Dec 2 '18 at 17:16


















$begingroup$
I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
$endgroup$
– Eric
Dec 2 '18 at 17:15




$begingroup$
I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
$endgroup$
– Eric
Dec 2 '18 at 17:15




1




1




$begingroup$
Why do you think the proof by Ted Shifrin assumes that the matrix is not defective? It seems to me that it works as written for all matrices (with the helpful explanation in the comment by MEB).
$endgroup$
– Alex Kruckman
Dec 2 '18 at 17:16






$begingroup$
Why do you think the proof by Ted Shifrin assumes that the matrix is not defective? It seems to me that it works as written for all matrices (with the helpful explanation in the comment by MEB).
$endgroup$
– Alex Kruckman
Dec 2 '18 at 17:16












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