A Factorization of Totally Positive Band Matrices

摘要

Every nonsingular totally positive m-banded matrix is shown to be the product of m totally positive one-banded matrices and, therefore, the limit of strictly m-banded matrices. This result is then extended to (bi) infinite 'nonsingular', totally positive matrices. In the process, such matrices are shown to possess at least one diagonal whose principal sections are all nonzero.(Author)