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Rayleigh quotient

For a given real symmetric matrix A and real nonzero vector x, the Rayleigh Quotient R(A,x) is defined as:

Note that R(A,c·x) = R(A,x) for any real scalar c. It can be shown that this quotient reaches its minimum value λ_min (the smallest eigenvalue of A) when x is v_min (the corresponding eigenvector). Similarly, R(A,x) ≤ λ_max and R(A,v_max) = λ_max

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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Rayleigh quotient".