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Companion matrices and their relations to Toeplitz and Hankel matrices

Yousong Luo, Robin Hill (2015)

Special Matrices

In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving...

Complementary matrices in the inclusion principle for dynamic controllers

Lubomír Bakule, José Rodellar, Josep M. Rossell (2003)

Kybernetika

A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary...

Complementary triangular forms

Rob Zuidwijk (1997)

Banach Center Publications

The notion of simultaneous reduction of pairs of matrices and linear operators to triangular forms is introduced and a survey of known material on the subject is given. Further, some open problems are pointed out throughout the text. The paper is meant to be accessible to the non-specialist and does not contain any new results or proofs.

Complete solution of tropical vector inequalities using matrix sparsification

Nikolai Krivulin (2020)

Applications of Mathematics

We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices by setting some of its entries to zero. All solutions are then combined to present the result in a...

Computation of linear algebraic equations with solvability verification over multi-agent networks

Xianlin Zeng, Kai Cao (2017)

Kybernetika

In this paper, we consider the problem of solving a linear algebraic equation A x = b in a distributed way by a multi-agent system with a solvability verification requirement. In the problem formulation, each agent knows a few columns of A , different from the previous results with assuming that each agent knows a few rows of A and b . Then, a distributed continuous-time algorithm is proposed for solving the linear algebraic equation from a distributed constrained optimization viewpoint. The algorithm is...

Computing generalized inverse systems using matrix pencil methods

Andras Varga (2001)

International Journal of Applied Mathematics and Computer Science

We address the numerically reliable computation of generalized inverses of rational matrices in descriptor state-space representation. We put particular emphasis on two classes of inverses: the weak generalized inverse and the Moore-Penrose pseudoinverse. By combining the underlying computational techniques, other types of inverses of rational matrices can be computed as well. The main computational ingredient to determine generalized inverses is the orthogonal reduction of the system matrix pencil...

Computing the determinantal representations of hyperbolic forms

Mao-Ting Chien, Hiroshi Nakazato (2016)

Czechoslovak Mathematical Journal

The numerical range of an n × n matrix is determined by an n degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an n degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus g = 1 . We reformulate the Fiedler-Helton-Vinnikov formulae for the genus g = 0 , 1 , and present an elementary computation...

Currently displaying 521 – 540 of 2599