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Order on Eigenvalues on Diagonal Matrix

Chloe Bennett • • 2 min read
Order on Eigenvalues on Diagonal Matrix
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If the eigenvalues are say $-1$, $-1$ and $2$ for a $3$ x $3$ matrix, then when comes to the diagonal matrix, is it (from top left, to bottom right) $-1$ $-1$ $2$ or $2$ $-1$ $-1$ or $-1$ $2$ $-1$? Does the order matter? How do you know what the order is?

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1 Answer

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It does not matter, it just has to be coherent with the order of the columns of $P$ in $A=PDP^{-1}$. In some applications we prefer to order the eigenvalues but in theory it's not necessary.

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Chloe Bennett
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Chloe Bennett

Chloe Bennett explores the intersection of pop culture, streaming entertainment, digital trends, and contemporary lifestyle. Her weekly commentary reaches thousands of culture enthusiasts.