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_reBXYg&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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I don't see anything wrong with this proof for a defective matrix. Is there a specific aspect you are concerned about? – Eric Dec 02 '18 at 17:15

1Why 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). – Alex Kruckman Dec 02 '18 at 17:16