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Let TH be the space of ( T + H)-matrices of order n. The paper considers the following question: Which unitary matrices U satisfy the condition ∀A ∈ TH → U* AU ∈ TH? A criterion for verifying whether a given matrix U has this property is proposed. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

The paper describes the congruent centralizer of the matrix $$ {\Delta}_n=\left(\begin{array}{llll}\hfill & \hfill & \hfill & 1\hfill \\ {}\hfill & \hfill & \dots \hfill & i\hfill \\ {}\hfill & 1\hfill & \dots \hfill & \hfill \\ {}1\hfill & i\hfill & \hfill & \hfill \end{array}\right) $$ , representing one of three blocks in the Horn-Sergeichuk canonical form, i.e., the set of matrices X such that X Δ X = Δ. [ABSTRACT FROM AUTHOR]

This paper shows that the stability or nonstability of switched systems does not depend on the eigenvalues of the matrices. The result is obtained by giving examples of no stable (resp. no unstable) switched linear systems consisting of stable (resp. unstable) matrices. Moreover, for the first time all kinds of eigenvalues are considered, as well as two general results for establishing the stability or nonstability of switched linear systems are presented. [ABSTRACT FROM AUTHOR]

The paper refines the classical Ostrowski disk theorem and suggests lower bounds for the smallest-in-modulus eigenvalue and the smallest singular value of a square matrix under certain diagonal dominance conditions. A lower bound for the smallest-in-modulus eigenvalue of a product of m ≥ 2 matrices satisfying joint diagonal dominance conditions is obtained. The particular cases of the bounds suggested that correspond to the infinity norm are discussed separately and compared with some known results. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]

The paper suggests sufficient nonsingularity conditions for matrices in terms of certain determinantal relations of diagonal dominance type, which improve and generalize some known results. These conditions are used to describe new eigenvalue inclusion sets and to derive new two-sided bounds on the determinants of matrices satisfying them. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]

The classes of right and left γ-generating matrices were introduced by D. Z. Arov in the 1980s. These matrices play an important role in the description of solutions of the indeterminate Nehari problem. In the present paper, the classes of the so-called generalized right and left γ-generating matrices, being resolvent matrices of the Nehari-Takagi problem, are introduced. For matrices of these classes, some factorization theorems are proved, and the connection between the class of generalized γ-generating matrices and the class of generalized j -inner matrix valued functions is found. Subclasses of singular, regular, and strongly regular generalized -generating matrices are introduced and studied. [ABSTRACT FROM AUTHOR]

The paper suggests method for computing points of the finite spectrum of a multiparameter matrix pencil (a multiparameter polynomial matrix linearly dependent on its parameters) of general form. At the first stage, a sequence { A + 휇 B} of pencils is computed, where B are constant matrices and A are ( q−k)-parameter matrices linearly dependent on parameters, k = 1,... q. At every step of the second stage, which is different for the regular and singular spectra, an auxiliary one- or two-parameter hereditary pencil is formed, and the points of its spectrum are computed. In order to determine whether the characteristics computed belong to spectru points of the original matrix, the hereditary pencils are used. Their construction is based on computing bases of null spaces of constant of one-parameter matrices (pencils). Bibliography: 5 titles. [ABSTRACT FROM AUTHOR]

In this paper, recently published results on matrix spectral factorization is reviewed, and their connection to wavelet matrices is revealed. [ABSTRACT FROM AUTHOR]

The determinant theory for matrices over a pseudo-complemented distributive lattice is presented. Previous results on this topic are special cases of the theorems proved in this paper. [ABSTRACT FROM AUTHOR]

In the present paper, a model of deformation of stochastic composites under microdamaging is developed for the case of orthotropic composite, when the microdamages are accumulated in the matrix. The composite is treated as an isotropic matrix strengthened by three-axial ellipsoidal inclusions with orthotropic symmetry of elastic properties. It is assumed that the loading process leads to accumulation of damages in the matrix. Fractured microvolumes are modeled by a system of randomly distributed quasispherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a composite with orthotropic components are taken as the basic relations. The fracture criterion is assumed to be given as the limit value of the intensity of average shear stresses occurring in the undamaged part of the material. Based on the analytical and numerical approach, an algorithm for the determination of nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the matrix. Using the numerical solution, nonlinear stress-strain diagrams for the orthotropic composite in the case of biaxial extension are obtained. [ABSTRACT FROM AUTHOR]

The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov’s theorem are analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles. [ABSTRACT FROM AUTHOR]

The paper demonstrates that in computing a linear form (g, x) on the solution of a system of linear equations Ax = f, the round-off error depends on the quantities ‖A−1f‖ and ‖AT−1g‖ rather than on the condition number of the coefficient matrix A. Estimates of the inherent and round-off errors in solving the above problem by the orthogonalization method are provided. Numerical results confirming theoretical conclusions are presented. Bibliography: 8 titles. [ABSTRACT FROM AUTHOR]

Two-sided bounds on | det A| for Nekrasov and S-Nekrasov matrices A are obtained. It is shown that for Nekrasov matrices the new bounds improve the known bounds of Bailey and Crabtree. As to the relatively recently introduced S-Nekrasov matrices, no bounds on their determinants have been suggested, as far as the author is aware. Bibliography: 13 titles. [ABSTRACT FROM AUTHOR]

The paper considers additive and multiplicative inverse eigenvalve problems and suggests a solution method based on the connection of inverse problems with the problem of computing the regular spectrum of a multiparameter pencil of constant matrices corresponding to the problem considered. Necessary and sufficient conditions for the solvability of inverse eigenvalve problems are established. Bibliography: 3 titles. [ABSTRACT FROM AUTHOR]

A complete description of the sets of pairs of anti-commuting Hankel matrices is given. [ABSTRACT FROM AUTHOR]

We consider properties of prime lattice matrices over the following lattices: chains, direct sums of chains, Boolean lattices. [ABSTRACT FROM AUTHOR]

We find a formula for the unique pseudoinverse of a normally solvable operator, establish conditions for the existence of a unique solution of a normally solvable equation, and obtain its representation in a Hilbert space. We also introduce the notion of one-sided pseudoinverse operators for normally solvable operators acting in Hilbert spaces and consider methods for their construction. [ABSTRACT FROM AUTHOR]

We study lower bounds on the number of nonzero entries in (0 , 1) matrices such that the permanent is always convertible to the determinant by placing ± signs on matrix entries. [ABSTRACT FROM AUTHOR]

Given a finite set {Ax}x ∈ X of nonnegative matrices, we derive joint upper and lower bounds for the row sums of the matrices D−1 A(x) D, x ∈ X, where D is a specially chosen nonsingular diagonal matrix. These bounds, depending only on the sparsity patterns of the matrices A(x) and their row sums, are used to obtain joint two-sided bounds for the Perron roots of given nonnegative matrices, joint upper bounds for the spectral radii of given complex matrices, bounds for the joint and lower spectral radii of a matrix set, and conditions sufficient for all convex combinations of given matrices to be Schur stable. Bibliography: 20 titles. [ABSTRACT FROM AUTHOR]

It is shown that the coneigenvalues of a matrix, when properly defined (in a way different from the one commonly used in the literature), obey relations similar to the classical inequalities between the (ordinary) eigenvalues and singular values. Several interesting spectral properties of conjugate-normal matrices are indicated. This matrix class plays the same role in the theory of unitary congruences as the class of normal matrices plays in the theory of unitary similarities. Bibliography: 5 titles. [ABSTRACT FROM AUTHOR]

Some statements of inverse eigenvalue problems for one-parameter and multiparameter regular polynomial matrices with linear and nonlinear dependences on spectral parameters are considered. Methods for solving inverse eigenvalue problems based on rank factorization, exhaustion, and reduction to nonlinear equations are proposed. Bibliography: 12 titles. [ABSTRACT FROM AUTHOR]

Implications related to the spectral decompositions of certain special Hankel matrices are derived from recent results of H. Rabe and A. C. M. Ran. Bibliography: 1 title. [ABSTRACT FROM AUTHOR]