The LU-factorization of totally positive matrices |
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Authors: | Colin W Cryer |
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Institution: | Oxford University Oxford, EnglandUK |
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Abstract: | An n × n real matrix A is an STP (strictly totally positive) matrix if all its minors are strictly positive. An n × n real triangular matrix A is a ΔSTP matrix if all its nontrivial minors are strictly positive. It is proved that A is an STP matrix iff A = LU where L is a lower triangular matrix, U is an upper triangular matrix, and both L and U are ΔSTP matrices. Several related results are proved. These results lead to simple proofs of many of the determinantal properties of STP matrices. |
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