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Transactions of the American Mathematical Society

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

 

 

The inverse of a totally positive bi-infinite band matrix


Author: Carl de Boor
Journal: Trans. Amer. Math. Soc. 274 (1982), 45-58
MSC: Primary 47B37; Secondary 15A09
MathSciNet review: 670917
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0670917-5
Keywords: Bi-infinite, matrix, total positivity, inverse, banded, main diagonal
Article copyright: © Copyright 1982 American Mathematical Society