Cullis-Radić determinant of a rectangular matrix which has a number of identical columns

In this paper we present how identical columns affect the Cullis-Radić determinant of an \(m\times n\) matrix, where \(m\leq n\).

A better heuristic approach for n-job m-machine flow shop scheduling problem

Scheduling problem has its origin in manufacturing industry.In this paper we describe a simple approach for solving the flow shop scheduling problem. The result we obtained has been compared with Palmers Heuristic and CDS algorithms along with NEH. It was found that our method will reach near optimum solution within few steps compared to CDS and NEHalgorithm and yield better result compared to Palmers Heuristic with objective of minimizing the Makespan for the horizontal rectangular matrix problems.

Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix

The article discusses the problem of solving a fully fuzzy linear system of equations with a fuzzy rectangular matrix and a fuzzy right-hand side described by fuzzy triangular numbers in a form of deviations from the mean. A solution algorithm based on finding pseudo-solutions of systems of linear equations and corresponding software is formed. Various examples of created software application for arbitrary fuzzy linear systems are given.

Perturbation bounds for the W-weighted core-EP inverse

In this paper, perturbation bounds are provided for the [Formula: see text]-weighted core-EP inverse of a rectangular matrix under reasonable conditions. Perturbation bounds for the core-EP inverse could be stated as a special case. Then, the continuity of the [Formula: see text]-weighted core-EP inverse is considered from the perspective of equations. Finally, we give an application to a semi-stable matrix involving an integral representation of the [Formula: see text]-weighted core-EP inverse of a perturbed matrix.

Some consequences of the rank normal form of a matrix

If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s = \left( {\matrix{ \hfill {{{\rm{I}}_{\rm{r}}}} & \hfill {\rm{O}} \cr \hfill {\rm{O}} & \hfill {\rm{O}} \cr } } \right) . This is the rank normal form of the matrix A. The purpose of this paper is to exhibit some consequences of this representation form.

Vector Spaces of Generalized Linearizations for Rectangular Matrix Polynomials

The complete eigenvalue problem associated with a rectangular matrix polynomial is typically solved via the technique of linearization. This work introduces the concept of generalized linearizations of rectangular matrix polynomials. For a given rectangular matrix polynomial, it also proposes vector spaces of rectangular matrix pencils with the property that almost every pencil is a generalized linearization of the matrix polynomial which can then be used to solve the complete eigenvalue problem associated with the polynomial. The properties of these vector spaces are similar to those introduced in the literature for square matrix polynomials and in fact coincide with them when the matrix polynomial is square. Further, almost every pencil in these spaces can be `trimmed' to form many smaller pencils that are strong linearizations of the matrix polynomial which readily yield solutions of the complete eigenvalue problem for the polynomial. These linearizations are easier to construct and are often smaller than the Fiedler linearizations introduced in the literature for rectangular matrix polynomials. Additionally, a global backward error analysis applied to these linearizations shows that they provide a wide choice of linearizations with respect to which the complete polynomial eigenvalue problem can be solved in a globally backward stable manner.