An innovative decomposition for inverting a nonsingular, asymmetric, and indefinite matrix [A] of order (n 脳 n) is derived in this paper. The inverse of [A] is written as [A]1 = [L][D][U] where [L] is a lower triangular matrix, [D] is a diagonal matrix, and [U] is an ...
Laplace−Kirchhoff matrices, perturbed by rooting a vertex by the unit element eij, have true inverses, which are combinations of unit matrices and partial inverses. The inverses are quadratic forms of matrices in the lower triangular form. At trees, they determine path coordinates of vertices. ...
A modification of the Ikebe algorithm for computing the lower half of the inverse of an (unreduced) upper Hessenberg matrix, extended to compute the entries of the superdiagonal, is considered in this paper. It enables us to compute the inverse of a quasiseparable Hessenberg matrix in O(n(2...