Generalization of some results concerning eigenvalues of a certain class of matrices and some applications

Mourad, Bassam

doi:10.1080/03081087.2012.746330

Cited by 14 publications

(6 citation statements)

References 24 publications

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“…Furthermore, combined matrices also appear in the chemistry field (see [2]). If we consider the case when C (A) is nonnegative, it has interesting properties and applications since it is a doubly stochastic matrix (see [3,4]).…”

Section: Introductionmentioning

confidence: 99%

Combined matrices of almost strictly sign regular matrices

Alonso

Peña

Serrano

2019

Journal of Computational and Applied Mathematics

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The combined matrix is a very useful concept for many applications. Almost strictly sign regular (ASSR) matrices form an important structured class of matrices with two possible zero patterns, which are either type-I staircase or type-II staircase. We prove that, under an irreducibility condition, the pattern of zero and nonzero entries of an ASSR matrix is preserved by the corresponding combined matrix. Without the irreducibility condition, it is proved that type-I and type-II staircases are still preserved. Illustrative numerical examples are included.

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Section: Introductionmentioning

confidence: 99%

Combined matrices of almost strictly sign regular matrices

Alonso

Peña

Serrano

2019

Journal of Computational and Applied Mathematics

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“…For instance, in [2], there are two applications, the first one concerning a topic in communication theory called satellite-switched and the second concerning a recent notion of doubly stochastic automorphism of a graph. In [14], some implications on nonnegative matrices and doubly stochastic matrices on graph theory, namely Graph spectra and Graph energy, are presented. In [3], conditions to obtain a nonnegative φ (A) are obtained.…”

Section: Introductionmentioning

confidence: 99%

CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) $$ A\circ A^{-T}$$

2019

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The Combined matrix of a nonsingular matrix A is defined by φ (A) = A • A −1 T where • means the Hadamard (entrywise) product. If the matrix A describes the relation between inputs and outputs in a multivariable process control, φ (A) describes the "relative gain array" (RGA) of the process and it defines the Bristol method [1] often used for Chemical processes [13, 15, 16]and [11, 8]. The combined matrix has been studied in several works such as [3], [6] and [10]. Since φ (A) = (c i j) has the property of ∑ k c ik = ∑ k c k j = 1, ∀i, j, when φ (A) ≥ 0, φ (A) is a doubly stochastic matrix. In certain chemical engineering applications a diagonal of the RGA in wchich the entries are near 1 is used to determine the pairing of inputs and outputs for further design analysis. Applications of these matrices can be found in Communication Theory, related with the satellite-switched time division multipleaccess systems, and about a doubly stochastic automorphism of a graph. In this paper we present new algorithms to generate doubly stochastic matrices with the Combined matrix using Hessenberg matrices in section 3 and orthogonal/unitary matrices in section 4. In addition, we discuss what kind of doubly stochastic matrices are obtained with our algorithms and the possibility of generating a particular doubly stochastic matrix by the map φ .

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“…For instance, in [5], there are two applications: the first one concerning a topic in communication theory called satellite-switched and the second concerning a recent notion of doubly stochastic automorphism of a graph. Recently, in [6], some implications on nonnegative matrices, doubly stochastic matrices, and graph theory, namely, graph spectra and graph energy, are presented.…”

Section: Introductionmentioning

confidence: 99%

Nonnegative Combined Matrices

Bru

Gassó

Giménez

et al. 2014

Journal of Applied Mathematics

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The combined matrix of a nonsingular real matrix is the Hadamard (entrywise) product ∘ ( −1 ) . It is well known that row (column) sums of combined matrices are constant and equal to one. Recently, some results on combined matrices of different classes of matrices have been done. In this work, we study some classes of matrices such that their combined matrices are nonnegative and obtain the relation with the sign pattern of . In this case the combined matrix is doubly stochastic.

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Generalization of some results concerning eigenvalues of a certain class of matrices and some applications

Cited by 14 publications

References 24 publications

Combined matrices of almost strictly sign regular matrices

Combined matrices of almost strictly sign regular matrices

CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) $$ A\circ A^{-T}$$

Nonnegative Combined Matrices

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