Summary about the research on the behavior of Evolution Strategies with positive definite quadratic forms (PDQFs) as fitness function. First the mutative self-adaptation ($\sigma$SA) is analyzed with focus on self-adaptation response and progress rates. For the latter, an optimal setting of the learning parameter is derived. If the learning parameter differs from the optimal setting mutative self-adaptation fails. Second the influence of noise on PDQFs is investigated. Formulae for progress rates and steady state distances are derived and compared to simulations. Additionally the equipartition conjecture is used to derive the steady state distances in the case of vanishing mutation strength. At last, the use of weighted recombination on PDQFs is theoretically analyzed and formulae for optimal weights are presented.