The eigenvalue based detection is a low-cost spectrum sensing method that detects the presence of primary user signal at a desired frequency. In this study, the largest eigenvalue distribution used in eigenvalue based detection methods is expressed using a new centering and scaling coefficients adjustment. Thus, the detection probability (P-d) and false detection probability (P-fa) equations for the maximum-minimum eigenvalue (MME), maximum eigenvalue to trace (MET) and maximum eigenvalue-geometric mean (ME-GM) have been obtained again. Weibull fading channels are the best model for wireless communication. For this reason, the studies were simulated in Weibull fading channels and analysed in detail with receiver operating characteristic curves (ROC). The results were compared with traditional methods and found to be more accurate.