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Mathematics-Online lexicon: Annotation to

Rayleigh Quotient


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Let $ S$ be a symmetric positive definite matrix. Then the extreme values of quotient

$\displaystyle r_S(x) = \frac{x^{\operatorname t}S x}{x^{\operatorname t}x},\quad x\ne 0\,
,
$

coincide with the smallest and the largest eigenvalue of $ S$.

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  automatisch erstellt am 19.  8. 2013