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Parameterization of totally positive matrices Previous Next Contents

4.ii. Parameterization of totally positive matrices

There is a very interesting a detailed theory of parameterizations of totally positive matrices TP [BFZ]. For our purposes, we select one particular parameterization. Let ai,j for i=1, 2, ..., m+p-1 and j < i be positive numbers. Let D1, D2, ..., Dm+p-1 be matrices with 1's on their diagonals and with the first upper diagonal of Di the sequence (ai,1, ai,2, ..., ai,i-1, 0, ..., 0). Then the product D1D2... Dm+p-1 is a matrix in TP, and the positive numbers ai,j parameterize TP.


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