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Negative Integral Powers of a Bidiagonal Matrix

Gurudas Chatterjee
Mathematics of Computation
Vol. 28, No. 127 (Jul., 1974), pp. 713-714
DOI: 10.2307/2005692
Stable URL: http://www.jstor.org/stable/2005692
Page Count: 2
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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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