<P> In mathematics, for a given complex Hermitian matrix M and nonzero vector x, the Rayleigh quotient R (M, x) (\ displaystyle R (M, x)), is defined as: </P> <Dl> <Dd> R (M, x): = x H M x x H x (\ displaystyle R (M, x): = (x ^ (\ text (H)) Mx \ over x ^ (\ text (H)) x)). </Dd> </Dl> <Dd> R (M, x): = x H M x x H x (\ displaystyle R (M, x): = (x ^ (\ text (H)) Mx \ over x ^ (\ text (H)) x)). </Dd> <P> For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose x H (\ displaystyle x ^ (\ text (H))) to the usual transpose x T (\ displaystyle x ^ (\ text (T))). Note that R (M, c x) = R (M, x) (\ displaystyle R (M, cx) = R (M, x)) for any non-zero real scalar c (\ displaystyle c). Also, recall that a Hermitian (or real symmetric) matrix has real eigenvalues . </P>

When is a matrix said to be self adjoint