Mathematics-Online lexicon: Sum and Product of Eigenvalues

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	Mathematics-Online lexicon:
	Sum and Product of Eigenvalues

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Let $\lambda_i$ denote the

not necessarily different eigenvalues of $n\times n$ matrix

. Then the follwing holds true:

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

Example:

automatically generated 6/25/2018