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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]

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]

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]

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]

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 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 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]