Negative integral powers of a bidiagonal matrix
Gurudas Chatterjee · Mathematics of Computation · 1974
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 ) ( - 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 ) (m - 1) of the diagonal elements, d i , d i + 1 , … , d j {d_i},{d_{i + 1}}, \ldots ,{d_j} , of the inverse matrix.