Abstract
An n × m real matrix A is a totally positive matrix if all its minors are nonnegative. The Neville elimination process is studied in relation to the existence of a totally positive factorization LS of a rectangular matrix. An LS factorization is obtained for a totally positive matrix, where L is a lower echelon form matrix, of size n × k, and S is an upper echelon form matrix, of size k × m, and both L and S are totally positive matrices.
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