Eigenvalue changes in sign when performed row operations.

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Eigenvalue of triangular matrix are elements in diagonal.



Now, consider the following matrix with eigenvalue $-5$ and $4$:
$$beginbmatrix
-4 & 2 \
4 & 3 \
endbmatrix$$
Now if I do row operation $R_2to R_2-(-R_1)$ and convert above matrix to following
$$beginbmatrix
-4 & 2 \
0 & 5 \
endbmatrix$$
The eigenvalue of this is $-4$, $5$



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




matrices eigenvalues-eigenvectors




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  • See math.stackexchange.com/questions/2160552/…
    – Robert Z
    yesterday






  • 4




    Possible duplicate of elementary row operation change the eigenvalue of a matrix
    – James
    yesterday










  • Why do you think that elementary row operations preserve eigenvalues?
    – amd
    10 hours ago














up vote
0
down vote

favorite












Eigenvalue of triangular matrix are elements in diagonal.



Now, consider the following matrix with eigenvalue $-5$ and $4$:
$$beginbmatrix
-4 & 2 \
4 & 3 \
endbmatrix$$
Now if I do row operation $R_2to R_2-(-R_1)$ and convert above matrix to following
$$beginbmatrix
-4 & 2 \
0 & 5 \
endbmatrix$$
The eigenvalue of this is $-4$, $5$



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




matrices eigenvalues-eigenvectors




share|cite|improve this question





















  • See math.stackexchange.com/questions/2160552/…
    – Robert Z
    yesterday






  • 4




    Possible duplicate of elementary row operation change the eigenvalue of a matrix
    – James
    yesterday










  • Why do you think that elementary row operations preserve eigenvalues?
    – amd
    10 hours ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Eigenvalue of triangular matrix are elements in diagonal.



Now, consider the following matrix with eigenvalue $-5$ and $4$:
$$beginbmatrix
-4 & 2 \
4 & 3 \
endbmatrix$$
Now if I do row operation $R_2to R_2-(-R_1)$ and convert above matrix to following
$$beginbmatrix
-4 & 2 \
0 & 5 \
endbmatrix$$
The eigenvalue of this is $-4$, $5$



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




matrices eigenvalues-eigenvectors




share|cite|improve this question













Eigenvalue of triangular matrix are elements in diagonal.



Now, consider the following matrix with eigenvalue $-5$ and $4$:
$$beginbmatrix
-4 & 2 \
4 & 3 \
endbmatrix$$
Now if I do row operation $R_2to R_2-(-R_1)$ and convert above matrix to following
$$beginbmatrix
-4 & 2 \
0 & 5 \
endbmatrix$$
The eigenvalue of this is $-4$, $5$



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





matrices eigenvalues-eigenvectors





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited yesterday









Robert Z

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  • See math.stackexchange.com/questions/2160552/…
    – Robert Z
    yesterday






  • 4




    Possible duplicate of elementary row operation change the eigenvalue of a matrix
    – James
    yesterday










  • Why do you think that elementary row operations preserve eigenvalues?
    – amd
    10 hours ago
















  • See math.stackexchange.com/questions/2160552/…
    – Robert Z
    yesterday






  • 4




    Possible duplicate of elementary row operation change the eigenvalue of a matrix
    – James
    yesterday










  • Why do you think that elementary row operations preserve eigenvalues?
    – amd
    10 hours ago















See math.stackexchange.com/questions/2160552/…
– Robert Z
yesterday




See math.stackexchange.com/questions/2160552/…
– Robert Z
yesterday




4




4




Possible duplicate of elementary row operation change the eigenvalue of a matrix
– James
yesterday




Possible duplicate of elementary row operation change the eigenvalue of a matrix
– James
yesterday












Why do you think that elementary row operations preserve eigenvalues?
– amd
10 hours ago




Why do you think that elementary row operations preserve eigenvalues?
– amd
10 hours ago















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