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.
linear-algebra matrices eigenvalues-eigenvectors
asked Dec 2 '18 at 16:37
AkhilAkhil
94
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add a comment |
$begingroup$
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.
linear-algebra matrices eigenvalues-eigenvectors
asked Dec 2 '18 at 16:37
AkhilAkhil
94
$endgroup$
$begingroup$
I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about?
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– Eric
Dec 2 '18 at 17:15
1
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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
add a comment |
$begingroup$
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.
linear-algebra matrices eigenvalues-eigenvectors
asked Dec 2 '18 at 16:37
AkhilAkhil
94
$endgroup$
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
linear-algebra matrices eigenvalues-eigenvectors
asked Dec 2 '18 at 16:37
AkhilAkhil
94
asked Dec 2 '18 at 16:37
AkhilAkhil
94
edited Dec 3 '18 at 5:44
Akhil
asked Dec 2 '18 at 16:37
AkhilAkhil
94
asked Dec 2 '18 at 16:37
AkhilAkhil
94
asked Dec 2 '18 at 16:37
AkhilAkhil
94
94
$begingroup$
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
add a comment |
$begingroup$
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
add a comment |
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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