Let A be an n × d matrix having full rank n. An orthogonal dual A of A is a (d − n) × d matrix of rank (d − n) such that every row of A is orthogonal (under the usual dot product) to every row of A. We define the orthogonal dual for arrangements by identifying an essential (central) arrangement of d hyperplanes in n-dimensional space with the n × d matrix of coefficients of the homogeneous line...

Using the continuous time algorithm given, the optimal is Absfract-This note studies the problem of decoupling in the linear, time invariant, multiinput-multioutput unity-feedback system. A parameterization of all stabilizing decoupling controllers and all achievable decoupled closed-loop transfer functions is obtained for full-row rank plants which do not have any coinciding poles and zeros in...

The implementation details of factorizing the 3 × 4 projection matrices of linear cameras into their left matrix factors and the 4 × 4 homogeneous central(also parallel for infinite center cases) projection factors are presented in this work. Any full row rank 3× 4 real matrix can be factorized into such basic matrices which will be called LC factors. A further extension to multiple view midpoi...

A signiicant collection of two-point boundary value problems is shown to give rise to linear systems of algebraic equations on which Gaussian elimination with row partial pivoting is unstable when standard solution techniques are used.

This paper proposes a distributed algorithm for multi-agent networks to achieve a minimum l1-norm solution to a linear equation Ax = b where A has full row rank. When the underlying network is undirected and fixed, it is proved that the proposed algorithm drive all agents’ individual states to converge in finite-time to the same minimum l1-norm solution. Numerical simulations are also provided ...

In this contribution, we present a formalization of the well-known Gauss-Jordan algorithm. It states that any matrix over a field can be transformed by means of elementary row operations to a matrix in reduced row echelon form. The formalization is based on the Rank Nullity Theorem entry of the AFP and on the HOL-Multivariate-Analysis session of Isabelle, where matrices are represented as funct...

In this paper we consider the problem of estimating simultaneously low-rank and row-wise sparse matrices from nested linear measurements where the linear operator consists of the product of a linear operatorW and a matrix Ψ . Leveraging the nested structure of the measurement operator, we propose a computationally efficient two-stage algorithm for estimating the simultaneously structured target...

We present an ordinary differential equations approach to the analysis of algorithms for constructing l1 minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The con...

Within the algebraic analysis approach to linear systems theory, a behaviour is the dual of the left module finitely presented by the matrix of functional operators defining the linear functional system. In this talk, we give an explicit characterization of isomorphic finitely presented modules, i.e., of isomorphic behaviours, in terms of certain inflations of their presentation matrices. Fitti...