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

DOI:
https://doi.org/10.1090/S0002-9947-1982-0670917-5

MathSciNet review:
670917

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Abstract: It is shown that a bounded bi-infinite banded totally positive matrix is boundedly invertible iff there is one and only one bounded sequence mapped by to the sequence . The argument shows that such a matrix has a main diagonal, i.e., the inverse of is the bounded pointwise limit of inverses of finite sections of principal with respect to a particular diagonal; hence or its inverse is again totally positive.

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Additional Information

DOI:
https://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