Linear algebra and its applications

Vol. 569, p. 1-14

DOI: 10.1016/j.laa.2018.12.035

Date of publication: 2019

Abstract:

This is a survey on some known properties of the possible Moore graph (or graphs) ¿ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition of ¿ induced by a vertex subset C, the following graphs are distance-regular: The induced graph of the vertices at distance 1 from C when C is a set of 400 independent vertices; the induced graphs of the vertices at distance 2 from C when C is a vertex or an edge, and the line graph of ¿. Besides, ¿ is an edge-distance-regular graph.]]>

Linear algebra and its applications

Vol. 559, p. 194-226

DOI: 10.1016/j.laa.2018.09.009

Date of publication: 2018-12-15

Abstract:

The classification of invariant subspaces is an open problem related to other important ones like the Carlson problem. Here we obtain a reduced form of these invariant subspaces as a new tool to tackle these problems. In particular, it allows us to prove quite easily partial results already known. The key point is assigning to each invariant subspace a marked one (its marked type) in order to partition the set of invariant subspaces in a finite number of subsets (the marked classes), each one containing only one marked subspace. Next, we parametrize (minimally) each marked class by means of the so-called PM reduced families, so that representatives of an invariant subspace (its PM reduced forms) appear in just one of these families.]]>

Linear algebra and its applications

DOI: 10.1016/j.laa.2018.10.015

Date of publication: 2018-10-22

Abstract:

In this work we introduce the triangular double sequences of arbitrary order given by linear recurrences, that generalize some well-known recurrences that appear in enumerative com- binatorics. In particular, we focussed on triangular sequences generated by two double sequences and establish their relation with the solution of linear three-term recurrences. We show through some simple examples how these triangular sequences appear as essential components in the expression of some clas- sical orthogonal polynomials and combinatorial numbers]]>

Linear algebra and its applications

DOI: 10.1016/j.laa.2018.01.026

Date of publication: 2018-02-01

Linear algebra and its applications

Vol. 536, p. 201-209

DOI: 10.1016/j.laa.2017.09.019

Date of publication: 2018-01-01

Abstract:

For each two-dimensional vector space V of commuting n×n matrices over a field F with at least 3 elements, we denote by V˜ the vector space of all (n+1)×(n+1) matrices of the form [A¿00] with A¿V. We prove the wildness of the problem of classifying Lie algebras V˜ with the bracket operation [u,v]:=uv-vu. We also prove the wildness of the problem of classifying two-dimensional vector spaces consisting of commuting linear operators on a vector space over a field.]]>

Linear algebra and its applications

Vol. 531, p. 210-219

DOI: 10.1016/j.laa.2017.05.046

Date of publication: 2017-10-15

Abstract:

Kautz digraphs K(d,l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz CK(d,l) and the subKautz sK(d,2) digraphs were recently introduced by Böhmová, Huemer and the author. In this paper we propose a new method to obtain the complete spectra of subKautz sK(d,2) and cyclic Kautz CK(d,3) digraphs, for all d=3, through the Hoffman–McAndrew polynomial and regular partitions. This approach can be useful to find the spectra of other families of digraphs with high regularity.]]>

Linear algebra and its applications

Vol. 527, p. 294-302

DOI: 10.1016/j.laa.2017.04.011

Date of publication: 2017-08-15

Abstract:

W.E. Roth (1952) proved that the matrix equation AX-XB=C has a solution if and only if the matrices View the MathML source and View the MathML source are similar. A. Dmytryshyn and B. Kågström (2015) extended Roth's criterion to systems of matrix equations View the MathML source(i=1,…,s) with unknown matrices X1,…,Xt, in which every Xs is X , X¿, or X¿. We extend their criterion to systems of complex matrix equations that include the complex conjugation of unknown matrices. We also prove an analogous criterion for systems of quaternion matrix equations.]]>

Linear algebra and its applications

Vol. 542, p. 402-421

DOI: 10.1016/j.laa.2017.06.010

Date of publication: 2017-06-12

Abstract:

We have named tridiagonal (p,r)–Toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi–periodic sequence, d(p+j)=rd(j), so with period p¿N but multiplied by a real number r. We present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout the discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear difference equations with quasi–periodic coefficients. The conditions that ensure the uniqueness solution of the boundary value problem lead us to the invertibility conditions for the matrix, whereas the solutions of the boundary value problems provides the entries of the inverse matrix.]]>

Linear algebra and its applications

Vol. 518, p. 97-143

DOI: 10.1016/j.laa.2016.12.032

Date of publication: 2017-04-01

Abstract:

Let p, m, n, d be positive integers and let Ln(d)Ln(d) denote the set of sequences L=(L1,…,Ln)L=(L1,…,Ln) of p×mp×m real or complex matrices which are realizable by systems of minimal order d. It was shown in ; that Ln(d)Ln(d) can be endowed with a structure of differentiable manifold when p=m=1p=m=1; that is, when the sequences are realizable by Single Input/Single Output (SISO) systems. In this paper a similar result is obtained for more general sequences. Specifically, we will consider the set View the MathML sourceLn(r_,s_) of sequences L which are realizable by systems of minimal order d and having View the MathML sourcer_ and View the MathML sources_ as Brunovsky indices of controllability and observability, respectively. It is shown in this paper that when one of the two collections of indices View the MathML sourcer_ or View the MathML sources_ is constant, then View the MathML sourceLn(r_,s_) can be provided with a structure of differentiable manifold and a formula of its dimension is given. The special cases View the MathML sourcer_=(1,…,1) or View the MathML sources_=(1,…,1) correspond to sequences realizable, respectively, by Single Input/Multi Output (SIMO) or Multi Input/Single Output (MISO) systems.]]>

Linear algebra and its applications

Vol. 529, p. 391-396

DOI: 10.1016/j.laa.2017.04.036

Date of publication: 2017

Abstract:

We show that the line digraph technique, when iterated, provides dense digraphs, that is, with asymptotically large order for a given diameter (or with small diameter for a given order). This is a well-known result for regular digraphs. In this note we prove that this is also true for non-regular digraphs.

We show that the line digraph technique, when iterated, provides dense digraphs, that is, with asymptotically large order for a given diameter (or with small diameter for a given order). This is a well- known result for regular digraphs. In this note we prove that this is also true for non-regular digraphs]]>

Linear algebra and its applications

Vol. 542, p. 624-647

DOI: 10.1016/j.laa.2017.12.009

Date of publication: 2017-01-01

Abstract:

© 2017 Elsevier Inc. We present a generalization of the theory of concatenated linear systems to commutative rings with identity. Moreover, we highlight sufficient conditions to obtain reachable and observable concatenated linear systems. This approach provides us with minimal input-state-output representations by means of which we can construct observable concatenated families of convolutional codes with different parameters over some particular rings. This work focuses on the characterization of models of serial, systematic serial and parallel concatenation.]]>

Linear algebra and its applications

Vol. 510, p. 246-258

DOI: 10.1016/j.laa.2016.08.022

Date of publication: 2016-12-01

Abstract:

The matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0 0 B are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) proved that the matrix equation X - AXB = C over a field has a solution if and only if the matrices A C 0 I and I 0 0 B are simultaneously equivalent to A 0 0 I and I 0 0 B . We extend these criteria to the matrix equations AX- ^ XB = C and X - A ^ XB = C over the skew field of quaternions with a fixed involutive automorphism q - ˆq.

The matrix equation AX-XB = C has a solution if and only if the matrices A C 0 B and A 0 0 B are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) proved that the matrix equation X - AXB = C over a field has a solution if and only if the matrices A C 0 I and I 0 0 B are simultaneously equivalent to A 0 0 I and I 0 0 B . We extend these criteria to the matrix equations AX- ^ XB = C and X - A ^ XB = C over the skew field of quaternions with a fixed involutive automorphism q ¿ ˆq.]]>

Linear algebra and its applications

Vol. 504, p. 325-353

DOI: 10.1016/j.laa.2016.04.011

Date of publication: 2016-09-01

Abstract:

We present a combinatorial study on the rearrangement of links in the structure of directed networks for the purpose of improving the valuation of a vertex or group of vertices as established by an eigenvector-based centrality measure. We build our topological classification starting from unidirectional rooted trees and up to more complex hierarchical structures such as acyclic digraphs, bidirectional and cyclical rooted trees (obtained by closing cycles on unidirectional trees). We analyze different modifications on the structure of these networks and study their effect on the valuation given by the eigenvector-based scoring functions, with particular focus on alpha-centrality and PageRank.

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/]]>

Linear algebra and its applications

Vol. 500, p. 52-62

DOI: 10.1016/j.laa.2016.03.014

Date of publication: 2016-07-01

Abstract:

A digraph Gamma = (V, E) is a line digraph when every pair of vertices u, v is an element of V have either equal or disjoint in -neighborhoods. When this condition only applies for vertices in a given subset (with at least two elements), we say that Gamma is a locally line digraph. In this paper we give a new method to obtain a digraph Gamma' cospectral with a given locally line digraph Gamma with diameter D, where the diameter D' of Gamma' is in the interval [D - 1, D + 1]. In particular, when the method is applied to De Bruijn or Kautz digraphs, we obtain cospectral digraphs with the same algebraic properties that characterize the formers. (C) 2016 Elsevier Inc. All rights reserved.]]>

Linear algebra and its applications

Vol. 493, p. 14-27

DOI: 10.1016/j.laa.2015.11.026

Date of publication: 2016-03-15

Abstract:

A characterization of hyperinvariant subspaces is given in terms of Weyr characteristic. Using this characterization we compute the number of the d-dimensional hyperinvariant subspaces.]]>

Linear algebra and its applications

Vol. 491, p. 419-433

DOI: 10.1016/j.laa.2015.11.012

Date of publication: 2016-02-15

Abstract:

Any elliptic operator defines an automorphism on the orthogonal subspace to the eigenfunctions associated with the lowest eigenvalue, whose inverse is the orthogonal Green operator. In this study, we show that elliptic Schrödinger operators on networks that have been obtained by adding a new vertex to a given network, can be seen as perturbations of the Schrödinger operators on the initial network. Therefore, the Green function of the new network can be computed in terms of the Green function of the original network.]]>

Linear algebra and its applications

Vol. 488, p. 363-376

DOI: 10.1016/j.laa.2015.09.053

Date of publication: 2016-01-01

Abstract:

As a generalization of orbit-polynomial and distance-regular graphs, we introduce the concept of a quotient-polynomial graph. In these graphs every vertex uinduces the same regular partition around u, where all vertices of each cell are equidistant from u. Some properties and characterizations of such graphs are studied. For instance, all quotient-polynomial graphs are walk-regular and distance-polynomial. Also, we show that every quotient-polynomial graph generates a (symmetric) association scheme.]]>

Linear algebra and its applications

Vol. 480, p. 115-126

DOI: 10.1016/j.laa.2015.04.020

Date of publication: 2015-05-16

Abstract:

Let the Kneser graph K of a distance-regular graph $\Gamma$ be the graph on the same vertex set as $\Gamma$, where two vertices are adjacent when they have maximal distance in $\Gamma$. We study the situation where the Bose-Mesner algebra of $\Gamma$ is not generated by the adjacency matrix of K. In particular, we obtain strong results in the so-called `half antipodal' case.]]>

Linear algebra and its applications

Vol. 472, p. 31-47

DOI: 10.1016/j.laa.2015.01.023

Date of publication: 2015-05-01

Abstract:

This paper deals with the question of completing a monotone increasing family of subsets Gamma of a finite set Omega to obtain the linearly dependent subsets of a family of vectors of a vector space. Specifically, we prove that such vectorial completions of the family of subsets Gamma exist and, in addition, we show that the minimal vectorial completions of the family Gamma provide a decomposition of the clutter Lambda of the inclusion-minimal elements of Gamma. The computation of such vectorial decomposition of clutters is also discussed in some cases. (C) 2015 Elsevier Inc. All rights reserved.]]>

Linear algebra and its applications

Vol. 468, p. 107-121

DOI: 10.1016/j.laa.2014.01.038

Date of publication: 2015-03-01

Abstract:

We consider here the discrete analogue of Serrin's problem: if the equilibrium measure of a network with boundary satisfies that its normal derivative is constant, what can be said about the structure of the network and the symmetry of the equilibrium measure? In the original Serrin's problem, the conclusion is that the domain is a ball and the solution is radial. To study the discrete Serrin's problem, we first introduce the notion of radial function and then prove a generalization of the minimum principle, which is one of the main tools in the continuous case. Moreover, we obtain similar results to those of the continuous case for some families of networks with a ball-like structure, which include spider networks with radial conductances, distance-regular graphs or, more generally, regular layered networks.]]>

Linear algebra and its applications

Vol. 468, p. 270-285

DOI: 10.1016/j.laa.2014.10.042

Date of publication: 2015

Linear algebra and its applications

Vol. 468, p. 38-47

DOI: 10.1016/j.laa.2013.12.039

Date of publication: 2015

Abstract:

A polyomino is an edge-connected union of cells in the planar square lattice. Here we consider generalized linear polyominoes; that is, the polyominoes supported by an n Ã— 2 lattice. In this paper, we obtain the Green function and the Kirchhoff index of a generalized linear polyomino as a perturbation of a 2n-path by adding weighted edges between opposite vertices. This approach deeply links generalized linear polyomino Green functions with the inverse M-matrix problem, and especially with the so-called Green matrices.

A polyomino is an edge-connected union of cells in the planar square lattice. Here we consider generalized linear polyominoes; that is, the polyominoes supported by an n Ã— 2 lattice. In this paper, we obtain the Green function and the Kirchhoff index of a generalized linear polyomino as a perturbation of a 2n-path by adding weighted edges between opposite vertices. This approach deeply links generalized linear polyomino Green functions with the inverse M-matrix problem, and especially with the so-called Green matrices.]]>

Linear algebra and its applications

Vol. 458, p. 245-250

DOI: 10.1016/j.laa.2014.06.001

Date of publication: 2014-10-01

Abstract:

The spectral excess theorem states that, in a regular graph Gamma, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency spectrum of Gamma), and Gamma is distance-regular if and only if equality holds. In this note we prove the corresponding result by using the Laplacian spectrum without requiring regularity of Gamma. (C) 2014 Elsevier Inc. All rights reserved.]]>

Linear algebra and its applications

Vol. 448, p. 11-21

DOI: 10.1016/j.laa.2014.02.003

Date of publication: 2014-05-01

Abstract:

We apply eigenvalue interlacing techniques for obtaining lower and upper bounds for the sums of Laplacian eigenvalues of graphs, and characterize equality. This leads to generalizations of, and variations on theorems by Crone, and Grone & Merris. As a consequence we obtain inequalities involving bounds for some well-known parameters of a graph, such as edge-connectivity, and the isoperimetric number. (C) 2014 Elsevier Inc. All rights reserved.]]>

Linear algebra and its applications

Vol. 442, p. 115-134

Date of publication: 2014

Linear algebra and its applications

Vol. 439, num. 12, p. 3945-3954

DOI: 10.1016/j.laa.2013.10.023

Date of publication: 2013-10-30

Abstract:

Let F be an arbitrary field, Mn(F) the set of all matrices n×n over F and J¿Mn(F) a Jordan matrix. In this paper, we obtain an explicit formula for the determinant of any matrix that commutes with J, i.e., the determinant of any element T¿Z(J), the centralizer of J. Our result can also be extended to any T'¿Z(A), where A¿Mn(F), can be reduced to J=S-1AS. This is because T=S-1T'S¿Z(J), and clearly View the MathML source. If F is algebraically closed, any matrix A can be reduced in this way to a suitable J. In order to achieve our main result, we use an alternative canonical form W¿Mn(F) called the Weyr canonical form. This canonical form has the advantage that all matrices K¿Z(W) are upper block triangular. The permutation similarity of T¿Z(J) and K¿Z(W) is exploited to obtain a formula for the determinant of T. The paper is organized as follows: Section 2 contains some definitions and notations that will be used through all the paper. In Section 3, matrices T¿Z(J) are described and the determinant of T is computed in a particular case. In Section 4, we recall the Weyr canonical form W of a matrix and the corresponding centralizer Z(W). A formula to compute the determinant of any K¿Z(W) is rewritten. Finally, in Section 5 an explicit formula for the determinant of any T¿Z(J) is obtained.

Let F be an arbitrary field, Mn(F) the set of all matrices n×n over F and J∈Mn(F) a Jordan matrix. In this paper, we obtain an explicit formula for the determinant of any matrix that commutes with J, i.e., the determinant of any element T∈Z(J), the centralizer of J. Our result can also be extended to any T′∈Z(A), where A∈Mn(F), can be reduced to J=S−1AS. This is because T=S−1T′S∈Z(J), and clearly View the MathML source. If F is algebraically closed, any matrix A can be reduced in this way to a suitable J. In order to achieve our main result, we use an alternative canonical form W∈Mn(F) called the Weyr canonical form. This canonical form has the advantage that all matrices K∈Z(W) are upper block triangular. The permutation similarity of T∈Z(J) and K∈Z(W) is exploited to obtain a formula for the determinant of T. The paper is organized as follows: Section 2 contains some definitions and notations that will be used through all the paper. In Section 3, matrices T∈Z(J) are described and the determinant of T is computed in a particular case. In Section 4, we recall the Weyr canonical form W of a matrix and the corresponding centralizer Z(W). A formula to compute the determinant of any K∈Z(W) is rewritten. Finally, in Section 5 an explicit formula for the determinant of any T∈Z(J) is obtained.]]>

Linear algebra and its applications

Vol. 439, num. 12, p. 3734-3745

DOI: 10.1016/j.laa.2013.10.025

Date of publication: 2013-10-26

Abstract:

Given a square matrix A, an A-invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T) that commute with A. Shoda's Theorem gives a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces for a nilpotent matrix in GF(2). Here we present an explicit construction for all subspaces of this type.

Given a square matrix A, an A-invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T) that commute with A. Shodaʼs Theorem gives a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces for a nilpotent matrix in GF(2). Here we present an explicit construction for all subspaces of this type.]]>

Linear algebra and its applications

Vol. 438, num. 5, p. 2484-2499

DOI: 10.1016/j.laa.2012.11.009

Date of publication: 2013-03-01

Linear algebra and its applications

Vol. 439, num. 7, p. 2070-2084

DOI: 10.1016/j.laa.2013.05.032

Date of publication: 2013

Linear algebra and its applications

Vol. 437, num. 5, p. 1285-1292

DOI: 10.1016/j.laa.2012.04.011

Date of publication: 2012-09

Abstract:

The main purpose of this paper is to study common invariant subspaces of any matrix in the centralizer of a given matrix A∈Mn(F), where F denotes an algebraically closed field. In particular, we obtain a necessary and sufficient condition for the existence of a common eigenvector for all the matrices in this set.]]>

Linear algebra and its applications

Vol. 436, num. 5, p. 1090-1098

DOI: 10.1016/j.laa.2011.06.044

Date of publication: 2012-03-01

Linear algebra and its applications

Vol. 437, num. 12, p. 2973-2977

DOI: 10.1016/j.laa.2012.07.019

Date of publication: 2012

Linear algebra and its applications

Vol. 4, num. 435, p. 884-901

DOI: 10.1016/j.laa.2011.02.014,

Date of publication: 2011-03-01

Abstract:

An algorithm to give an explicit description of all the solutions to any tropical linear system A⊙x=B⊙x is presented. The given system is converted into a finite (rather small) number p of pairs (S,T) of classical linear systems: a system S of equations and a system T of inequalities. The notion, introduced here, that makes p small, is called compatibility. The particular feature of both S and T is that each item (equation or inequality) is bivariate, i.e., it involves exactly two variables; one variable with coefficient 1 and the other one with -1. S is solved by Gaussian elimination. We explain how to solve T by a method similar to Gaussian elimination. To achieve this, we introduce the notion of sub-special matrix. The procedure applied to T is, therefore, called sub-specialization.]]>

Linear algebra and its applications

Vol. 434, num. 5, p. 1325-1335

DOI: 10.1016/j.laa.2010.11.009

Date of publication: 2011

Abstract:

It is well known that, when a full rank observable pair (C,A) is slightly perturbed, the new observability indices k′ are majorized by the initial ones k, k≻k′. Conversely, any indices k′ majorized by k can be obtained by perturbing (C,A). The aim of this paper is the explicit construction of perturbations of (C,A) which have the desired indices k′ by means of a sequence of uniparametrical versal perturbations. Even more, using versal deformations we refine this construction in such a way that the perturbation has the maximum possible number of zeros and no parameters in the square part.]]>

Linear algebra and its applications

Vol. 435, num. 10, p. 2626-2638

DOI: 10.1016/j.laa.2011.05.004

Date of publication: 2011

Linear algebra and its applications

Vol. 433, num. 11-12, p. 1821-1826

DOI: 10.1016/j.laa.2010.06.042

Date of publication: 2010-12-30

Abstract:

A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ between any pair of vertices at distance $j\in [0,m]$ depends only on the values of $i$ and $j$. In this paper we study some algebraic and combinatorial characterizations of $(\ell,m)$-walk-regularity based on the so-called predistance polynomials and the preintersection numbers.]]>

Linear algebra and its applications

Vol. 432, num. 9, p. 2278-2292

DOI: 10.1016/j.laa.2009.05.032

Date of publication: 2010-04-15

Abstract:

In this work we define the effective resistance between any pair of vertices with respect to a value λ ≥ 0 and a weight ω on the vertex set. This allows us to consider a generalization of the Kirchhoff Index of a finite network. It turns out that λ is the lowest eigenvalue of a suitable semi-definite positive Schrödinger operator and ω is the associated eigenfunction. We obtain the relation between the effective resistance, and hence between the Kirchhoff Index, with respect to λ and ω and the eigenvalues of the associated Schrödinger operator. However, our main aim in this work is to get explicit expressions of the above parameters in terms of equilibrium measures of the network. From these expressions, we derive a full generalization of Foster’s formulae that incorporate a positive probability of remaining in each vertex in every step of a random walk. Finally, we compute the effective resistances and the generalized Kirchhoff Index with respect to a λ and ω for some families of networks with symmetries, specifically for weighted wagon-wheels and circular ladders.]]>

Linear algebra and its applications

Vol. 432, num. 9, p. 2418-2422

DOI: 10.1016/j.laa.2009.07.030

Date of publication: 2010-04-15

Abstract:

The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role.]]>

Linear algebra and its applications

Vol. 432, num. 9, p. 2438-2454

DOI: 10.1016/j.laa.2009.11.008

Date of publication: 2010-04-15

Linear algebra and its applications

Vol. 433, p. 1821-1826

DOI: 10.1016/j.laa.2010.06.042

Date of publication: 2010

Linear algebra and its applications

Vol. 430, num. 5-6, p. 1574-1589

DOI: 10.1016/j.laa.2008.04.033

Date of publication: 2009-03

Abstract:

Specific algorithms, such as those involving the supremal of the invariant subspaces contained in a suitable subspace, are known to be able to test whether a disturbance decoupling problem (DDP) is solvable. Here, by reducing the system to its Molinari form, we obtain an alternative description of this supremal object and compute its dimension. Hence we have a general result for solving the decoupling provided that a Molinari basis is known. In particular, a necessary numerical condition for it is derived. The same technique is applied to the DDPS, that is, when stability of the decoupled closed loop system is required.]]>

Linear algebra and its applications

Vol. 430, num. 4, p. 1336-1349

DOI: 10.1016/j.laa.2008.10.027

Date of publication: 2009-02

Linear algebra and its applications

Vol. 429, num. 7, p. 1823-1839

Date of publication: 2008-10

Linear algebra and its applications

Vol. 429, num. 5-6, p. 1102-1113

Date of publication: 2008-09

Linear algebra and its applications

Vol. 428, num. 7, p. 1499-1510

Date of publication: 2008-04

Linear algebra and its applications

Vol. 423, num. 1, p. 109-118

DOI: 10.1016/j.laa.2006.11.018

Date of publication: 2007-05

Linear algebra and its applications

Vol. 423, num. 1, p. 74-80

Date of publication: 2007-05

Linear algebra and its applications

Vol. 421, num. 1, p. 45-52

DOI: 10.1016/j.laa.2006.07.028

Date of publication: 2007-02

Linear algebra and its applications

Vol. 419, num. 1, p. 234-250

Date of publication: 2006-11

Linear algebra and its applications

Vol. 416, num. 2-3, p. 355-364

Date of publication: 2006-07