Hi Nona,
When analyzing first-order kinetic data, the concentration profiles of different samples over time are all proportional to the same exponential decay function, differing only by their initial concentrations. This means that the data matrix constructed from such measurements has rank 1, as all rows are scalar multiples of a single vector. When the data is mean-centered—by subtracting the mean value at each time point across all samples—the proportionality among the rows is preserved (unless all samples are identical, in which case the matrix becomes all zeros and the rank drops to 0). As a result, the mean-centered data matrix still has rank 1. In principal component analysis (PCA), this means that only the first principal component will capture all the variance in the data, reflecting the underlying single kinetic process driving the system.
