The inverse of a totally positive bi-infinite band matrix

de Boor, Carl

doi:10.1090/S0002-9947-1982-0670917-5

The inverse of a totally positive bi-infinite band matrix
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by Carl de Boor

Trans. Amer. Math. Soc. 274 (1982), 45-58

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

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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.

References

What is the main diagonal of a biifinite band matrix?

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