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Eigenvalue of triangular matrix are elements in diagonal.

Now, consider the following matrix with eigenvalue $-5$ and $4$: $$\begin{bmatrix} -4 & 2 \\ 4 & 3 \\ \end{bmatrix}$$ Now if I do row operation $R_2\to R_2-(-R_1)$ and convert above matrix to following $$\begin{bmatrix} -4 & 2 \\ 0 & 5 \\ \end{bmatrix}$$ The eigenvalue of this is $-4$, $5$

First one is correct, what is wrong with the second one?

Robert Z
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vikram barandwal
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  • See https://math.stackexchange.com/questions/2160552/elementary-row-operation-change-the-eigenvalue-of-a-matrix – Robert Z Aug 05 '18 at 08:47
  • Why do you think that elementary row operations preserve eigenvalues? – amd Aug 05 '18 at 23:48

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