  We give both lower and upper estimates for eigenvalues of unbounded positive
definite operators in an arbitrary Hilbert space. We show scaling robust
relative eigenvalue estimates for these operators in analogy to such estimates
of current interest in Numerical Linear Algebra. Only simple matrix theoretic
tools like Schur complements have been used. As prototypes for the strength of
our method we discuss a singularly perturbed Schroedinger operator and study
convergence estimates for finite element approximations. The estimates can be
viewed as a natural quadratic form version of the celebrated Temple--Kato
inequality.
