Rayleigh quotient

Common card · No. 326599

In mathematics, the Rayleigh quotient () for a given complex Hermitian matrix M {\displaystyle M} and nonzero vector x {\displaystyle x} is defined as R ( M , x ) = x ∗ M x x ∗ x . {\displaystyle R(M,x)={\frac {x^{*}Mx}{x^{*}x}}.} For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose x ∗ {\displaystyle x^{*}}...