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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The inverse of a totally positive bi-infinite band matrix
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by Carl de Boor PDF
Trans. Amer. Math. Soc. 274 (1982), 45-58 Request permission

Abstract:

It is shown that a bounded bi-infinite banded totally positive matrix $A$ is boundedly invertible iff there is one and only one bounded sequence mapped by $A$ to the sequence $({( - )^i})$. The argument shows that such a matrix has a main diagonal, i.e., the inverse of $A$ is the bounded pointwise limit of inverses of finite sections of $A$ principal with respect to a particular diagonal; hence $({( - )^{i + j}}{A^{ - 1}}(i,j))$ or its inverse is again totally positive.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 274 (1982), 45-58
  • MSC: Primary 47B37; Secondary 15A09
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0670917-5
  • MathSciNet review: 670917