Rayleigh's Principle

A variational estimate for the fundamental eigenvalue of a symmetric positive‑definite generalized eigenproblem K φ = λ M φ (e.g., structural vibration), expressed by the Rayleigh quotient R(u) = (uᵀ K u)/(uᵀ M u); the minimum of R over admissible, nonzero trial vectors u equals the smallest eigenvalue, and any admissible trial produces an estimate that is greater than or equal to that true fundam