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Mathematics of Computation

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Negative integral powers of a bidiagonal matrix


Author: Gurudas Chatterjee
Journal: Math. Comp. 28 (1974), 713-714
MSC: Primary 65F30
DOI: https://doi.org/10.1090/S0025-5718-1974-0371049-5
MathSciNet review: 0371049
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Abstract: The elements of the inverse of a bidiagonal matrix have been expressed in a convenient form. The higher negative integral powers of the bidiagonal matrix exhibit an interesting property: the (ij)th element of the $ ( - m)$th power is equal to the product of the corresponding element of the inverse by a Wronski polynomial, viz., the complete symmetric function of degree $ (m - 1)$ of the diagonal elements, $ {d_i},{d_{i + 1}}, \ldots ,{d_j}$, of the inverse matrix.


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DOI: https://doi.org/10.1090/S0025-5718-1974-0371049-5
Article copyright: © Copyright 1974 American Mathematical Society