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Mathematics-Online lexicon:

Sum and Product of Eigenvalues


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Let $ \lambda_i$ denote the $ n$ not necessarily different eigenvalues of $ n\times n$ matrix $ A$. Then the follwing holds true:

$\displaystyle \sum_{i=1}^n \lambda_i = \operatorname{Sp}(A),\quad
\prod_{i=1}^n \lambda_i = \operatorname{det}(A)
\,.
$

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  automatically generated 6/25/2018