scholarly journals A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices

2016 ◽  
Vol 2016 ◽  
pp. 1-3 ◽  
Author(s):  
Hal Caswell ◽  
Silke F. van Daalen
Keyword(s):  
Simple Formula ◽  
Column Vector ◽  
Structured Matrices ◽  
Structured Matrix ◽  
Block Structured

The vec operator transforms a matrix to a column vector by stacking each column on top of the next. It is useful to write the vec of a block-structured matrix in terms of the vec operator applied to each of its component blocks. We derive a simple formula for doing so, which applies regardless of whether the blocks are of the same or of different sizes.

scholarly journals Well-solvable cases of the QAP with block-structured matrices

2015 ◽  
Vol 186 ◽  
pp. 56-65 ◽  
Author(s):  
Eranda Çela ◽  
Vladimir G. Deineko ◽  
Gerhard J. Woeginger
Keyword(s):  
Structured Matrices ◽  
Block Structured

Structured matrix norms for robust stability and performance with block-structured uncertainty

1998 ◽  
Vol 71 (4) ◽  
pp. 535-557 ◽  
Author(s):  
Vijaya-Sekhar Chellaboina ◽  
Wassim M. Haddad ◽  
Dennis S. Bernstein
Keyword(s):  
Robust Stability ◽  
Structured Uncertainty ◽  
Structured Matrix ◽  
And Performance ◽  
Matrix Norms ◽  
Block Structured

Structured matrix norms for real and complex block-structured uncertainty

Automatica ◽  
1997 ◽  
Vol 33 (5) ◽  
pp. 995-997 ◽  
Author(s):  
Vijaya-Sekhar Chellaboina ◽  
Wassim M. Haddad
Keyword(s):  
Structured Uncertainty ◽  
Structured Matrix ◽  
Matrix Norms ◽  
Complex Block ◽  
Block Structured

Some Properties of the Exchange Operator with respect to Structured Matrices defined by Indefinite Scalar Product Spaces

2015 ◽  
Vol 30 ◽  
Author(s):  
Hanz Martin Cheng ◽  
Roden Jason David
Keyword(s):  
Scalar Product ◽  
Structured Matrices ◽  
Product Spaces ◽  
Orthogonal Matrices ◽  
Structured Matrix ◽  
Exchange Operator ◽  
Siam Review

The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)×(p+q) and exc : M ×N×N → M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504–519, 2003.].

scholarly journals Some efficient methods for computing the determinant of large sparse matrices

2014 ◽  
Vol Volume 17 - 2014 - Special... ◽  
Author(s):  
Emmanuel Kamgnia ◽  
Louis Bernard Nguenang
Keyword(s):  
Complex Plane ◽  
Sparse Matrices ◽  
Grand Nombre ◽  
Nous Proposons ◽  
Integration Process ◽  
Scientific Applications ◽  
Structured Matrix ◽  
International Audience ◽  
Block Structured ◽  
Large Sparse Matrices

International audience The computation of determinants intervenes in many scientific applications, as for example in the localization of eigenvalues of a given matrix A in a domain of the complex plane. When a procedure based on the application of the residual theorem is used, the integration process leads to the evaluation of the principal argument of the complex logarithm of the function g(z) = det((z + h)I - A)/ det(zI - A), and a large number of determinants is computed to insure that the same branch of the complex logarithm is followed during the integration. In this paper, we present some efficient methods for computing the determinant of a large sparse and block structured matrix. Tests conducted using randomly generated matrices show the efficiency and robustness of our methods. Le calcul de déterminants intervient dans certaines applications scientifiques, comme parexemple dans le comptage du nombre de valeurs propres d’une matrice situées dans un domaineborné du plan complexe. Lorsqu’on utilise une approche fondée sur l’application du théorème desrésidus, l’intégration nous ramène à l’évaluation de l’argument principal du logarithme complexe de lafonction g(z) = det((z + h)I − A)/ det(zI − A), en un grand nombre de points, pour ne pas sauterd’une branche à l’autre du logarithme complexe. Nous proposons dans cet article quelques méthodesefficaces pour le calcul du déterminant d’une matrice grande et creuse, et qui peut être transforméesous forme de blocs structurés. Les résultats numériques, issus de tests sur des matrices généréesde façon aléatoire, confirment l’efficacité et la robustesse des méthodes proposées.

scholarly journals Block Representation and Spectral Properties of Constant Sum Matrices

2018 ◽  
Vol 34 ◽  
pp. 170-190 ◽  
Author(s):  
Sally Hill ◽  
Matthew Lettington ◽  
Karl Michael Schmidt
Keyword(s):  
Spectral Properties ◽  
Structured Matrices ◽  
Eigenvalues And Eigenvectors ◽  
Equivalent Representation ◽  
Symmetry Properties ◽  
Explicit Formulae ◽  
Block Structured

An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.

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