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the order of eigenvalues is important, but when you calculate an eigenvalue polynomial i am still not aware of any rule that dictates which eigenvalue comes first and which does not. let me explain what i mean. take the matrix

[tex]

\begin{bmatrix}

3 & -2 \\

5 & -4

\end{bmatrix}

[/tex]

The eigenvalues are -2, and 1

I forget the technical name but when you construct a matrix composed of eigenvalues you can have either

[tex]

\begin{bmatrix}

-2 & 0 \\

0 & 1

\end{bmatrix}

[/tex]

or

[tex]

\begin{bmatrix}

1 & 0 \\

0 & -2

\end{bmatrix}

[/tex]

There's a big difference between those two matrices so which one is correct? Up until now it seems that the larger number always occupies the upper left corner but i haven't been paying much attention to it.

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# Homework Help: The order of eigenvalues

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