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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 overview

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$.
(Authors: App/Burkhardt/Höllig)



  automatically generated 3/16/2005