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Mathematics-Online course: Linear Algebra - Normal Forms - Diagonalisation

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$.
(Authors: App/Burkhardt/Höllig)

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  automatically generated 4/21/2005