Many methods have been proposed in the last few years for the study of the identifiability of linear systems. We review these methods, which are based on different basic concepts, and demonstrate that these approaches can be considered as equivalent and that some properties are common. We use these results to study the relations between the determinants of the jacobian matrices corresponding to these approaches. The calculation of these determinants has a great importance since the jacobian matrices are the main starting points for the study of local identifiability and are proposed by some authors for the study of global identifiability. However, whatever the method used, this calculation is long, often difficult and even unmanageable when the model is too complex. We show that the relations between the model parameters that negate these determinants can be determinated from the study of some matrices that have the same rank properties as jacobian matrices, and whose main interest is that they are easy to obtain and available even in the case of complex models.