Square matrix

About: Square matrix is a research topic. Over the lifetime, 5000 publications have been published within this topic receiving 92428 citations.

Matrix print rotation

Abstract: A printer using a matrix of printing elements arranged in a square configuration with the printing elements being used to print alpha-numeric data in either a vertical or horizontal orientation by electronically selecting a rectangular matrix from less than the full number of printing elements in the square matrix to permit selective orientation of the printed data without mechanically reorienting the print head. The print element drive circuitry also enables the printing matrix to print from either end of the selected rectangular print matrix in either the horizontal or vertical orientation to provide four possible orientations of the printed alpha-numeric data. A memory is used to store the input control signals for each of the rows of the rectangular printing matrix while a control means is provided for reading out the control signals in either direction from the memory in combination with a matrix selection control to provide energization of a rectangular print matrix in either the horizontal or vertical configuration.

Inverse spectral problems for difference operators with rational scattering matrix function

Abstract: In this paper we obtain explicit formulas for the coefficients of a second order difference block operator if its spectral or its scattering functions are rational matrix functions analytic and invertible on the unit circle. The solutions are given in terms of realizations of the spectral or scattering function.

On the Computation of Null Spaces of Sparse Rectangular Matrices

Abstract: Computing the null space of a sparse matrix is an important part of some computations, such as embeddings and parametrization of meshes We propose an efficient and reliable method to compute an orthonormal basis of the null space of a sparse square or rectangular matrix (usually with more rows than columns) The main computational component in our method is a sparse $LU$ factorization with partial pivoting of the input matrix; this factorization is significantly cheaper than the $QR$ factorization used in previous methods The paper analyzes important theoretical aspects of the new method and demonstrates experimentally that it is efficient and reliable

Linear complementarity as absolute value equation solution

Abstract: We consider the linear complementarity problem (LCP): $$Mz+q\ge 0, z\ge 0, z^{\prime }(Mz+q)=0$$ as an absolute value equation (AVE): $$(M+I)z+q=|(M-I)z+q|$$ , where $$M$$ is an $$n\times n$$ square matrix and $$I$$ is the identity matrix. We propose a concave minimization algorithm for solving (AVE) that consists of solving a few linear programs, typically two. The algorithm was tested on 500 consecutively generated random solvable instances of the LCP with $$n=10, 50, 100, 500$$ and 1,000. The algorithm solved $$100\,\%$$ of the test problems to an accuracy of $$10^{-8}$$ by solving 2 or less linear programs per LCP problem.