Mathematics-Online lexicon: Rayleigh Quotient

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	Mathematics-Online lexicon:
	Rayleigh Quotient

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

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

(Authors: App/Burkhardt/Höllig)

see also:

automatically generated 3/16/2005