In helioseismic inversions, the number of independent pieces of information that a mode set contains is much less than the actual number of modes. This is due in part to the similarity between the basis functions that define the inverse problem, the kernels, while the observational errors also contribute to the loss of independent information. We have devised a strategy to assess the amount of independent and accessible information contained in a given mode set. It consists in calculating the number of linearly independent data, that is the number of modes that cannot be obtained as linear combinations of the others. We have restricted our analysis to the solar stratification inverse problem. It turns out that within the present observational errors, only a small amount of modes are linearly independent. Indeed, if we use a SOI/MDI data set of 1560 modes, only 117 were independent. Although this result might appear discouraging indicating an apparent substantial loss of useful information, it also allow us to reparameterize the data set before the inversion is carried out. Such reparameterization considerably reduce the computation burden of such inversion.