Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...

This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix [G | I]. The advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure, for different input matrices. In particular, we derive representa...

In this paper, we import interval method to the iteration for computing Moore-Penrose inverse of the full row (or column) rank matrix. Through modifying the classical Newton iteration by interval method, we can get better numerical results. The convergence of the interval iteration is proven. We also give some numerical examples to compare interval iteration with classical Newton iteration.

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matr...

Utilizing the Moore-Penrose generalized inverse of the Jacobian matrix of wire-actuated parallel robot manipulators, one or more wire tensions could be negative. In this paper, a methodology for calculating positive wire tensions, with minimum 2-norm for tension vector, is presented. A planar parallel manipulator is simulated to illustrate the proposed methodology.

We analyze when the Moore–Penrose inverse of the combinatorial Laplacian of a distance– regular graph is a M–matrix; that is, it has non–positive off–diagonal elements. In particular, our results include some previously known results on strongly regular graphs.

In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.

We prove some identities related to the reverse order law for the Moore-Penrose inverse of operators on Hilbert spaces, extending some results from (Y. Tian and S. Cheng, Linear Multilinear Algebra 52 (2004)) and (R. E. Cline, SIAM Review, Vol. 6, No. 1 (1964)) to infinite dimensional settings. 2010 Mathematics Subject Classification: 47A05, 15A09.

Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.