Rayleigh quotient
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