Main Page | See live article | Alphabetical index In mathematics, 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 λmin (the smallest eigenvalue of A) when x is vmin (the corresponding eigenvector). Similarly, R(A,x) ≤ λmax and R(A,vmax) = λmax This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.