The Best Possible Bounds for Full Rank Probability of a Random Submatroid

We give a new proof of (the sharpest at present) attainable and effectively computable lower bounds for full rank probability of a random submatroid, which were previously obtained by the author. The proof reveals the nature of these bounds and involves majorization theory methods of deriving inequalities in constructing such bounds. The comparison of the obtained bounds with other attainable ones for the characteristic under estimation is given.