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On Game Problems of Controlling Pencil Trajectories under Integral Constraints on the Controls of Players
AbstractThe game problems of control of pencil trajectories, described by a system of equations with a retarded argument under integral restrictions...
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The Vandermonde Matrix in the Commutative Case
AbstractIn a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde...
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Strong Dissipative Hydrodynamical Systems and the Operator Pencil of S. Krein
AbstractThis review paper is devoted to the description of the results of N.D. Kopachevsky and S. Krein (form 1964 till nowadays) related to spectral...
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Realizations of Non-commutative Rational Functions Around a Matrix Centre, II: The Lost-Abbey Conditions
In a previous paper the authors generalized classical results on minimal realizations of non-commutative (nc) rational functions, using nc...
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Elementary Operations and Matrix Invariants
In the previous chapter, we learned the matrix representation \(\boldsymbol{A}\)...
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Algorithm for Separating Matrix Spectrum by an Angle
AbstractAn algorithm for separating the matrix spectrum by a piecewise-smooth curve, namely, by an angle, is presented. A complete description of the...
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The Exponential of a Matrix
Covers matrix exponentials, and how to calculate them, as the key to solving linear systems with constant coefficients. Systems with variable...
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Pseudospectra of Loewner Matrix Pencils
Loewner matrix pencils play a central role in the system realization theory of Mayo and Antoulas, an important development in data-driven modeling....
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Low-Rank Perturbation of Regular Matrix Pencils with Symmetry Structures
The generic change of the Weierstraß canonical form of regular complex structured matrix pencils under generic structure-preserving additive low-rank...
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Recovering a perturbation of a matrix polynomial from a perturbation of its first companion linearization
A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory,...
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Matrix compression along isogenic blocks
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation...
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Bisector fields and pencils of conics
We introduce the notion of a bisector field, which is a maximal collection of pairs of lines such that for each line in each pair, the midpoint of...
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High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method
The Gerdjikov-Ivanov (GI) hierarchy is derived via recursion operator, in this article, we mainly investigate the third-order flow GI equation. In...
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Generating Systems of the Full Matrix Algebra That Contain Nonderogatory Matrices
Let 𝒜 be an algebra over a field 𝔽 generated by a set of matrices 𝒮. The paper considers algorithmic aspects of checking whether 𝒜 coincides with...
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Jordan–Kronecker Invariants for Lie Algebras of Small Dimensions
In this paper, Jordan–Kronecker invariants are calculated for all nilpotent 6- and 7-dimensional Lie algebras. We consider the Poisson bracket...
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Computing the distance to continuous-time instability of quadratic matrix polynomials
A bisection method is used to compute lower and upper bounds on the distance from a quadratic matrix polynomial to the set of quadratic matrix...
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A Three-Dimensional Generalization of QRT Maps
We propose a geometric construction of three-dimensional birational maps that preserve two pencils of quadrics. The maps act as compositions of...
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The Rational Interpolation Problem: Grassmannian and Loewner-Matrix Approaches
We review the Grassmannian approach to rational interpolation theory and indicate points of contact and divergence with the Loewner-matrix approach....