The approximation of a totally positive band matrix by a strictly banded totally positive one |
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Authors: | Carl de Boor Allan Pinkus |
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Institution: | Mathematics Research Center University of Wisconsin—Madison Madison, Wisconsin 53706, USA;Department of Mathematics Technion Haifa, Israel |
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Abstract: | 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 totally positive matrices. This result is then extended to (bi)infinite m-banded totally positive matrices with linearly independent rows and columns. In the process, such matrices are shown to possess at least one diagonal whose principal sections are all nonzero. As a consequence, such matrices are seen to be approximable by strictly m-banded totally positive ones. |
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