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Further Investigation of Positive Semi-definiteness of Fourth-order Cauchy and Hilbert Tensors
In this paper, we further investigate the positive (semi-)definiteness of even order tensors. For the fourth-order tensor, we discuss the...
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The Collatz-Wielandt Quotient for Pairs of Nonnegative Operators
In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators A, B that map a given pointed generating...
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Descriptor Systems Under Feedback and Output Injection
In this paper we study simultaneous feedback and output injection on descriptor linear system described by a quadruple of matrices (E,A,B,C). We...
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On nilpotent Chernikov p-groups with elementary tops
The description of nilpotent Chernikov p -groups with elementary tops is reduced to the study of tuples of skew-symmetric bilinear forms over the...
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Equivalences of matrix polynomials
We investigate whether variants of equivalence of (singular) matrix polynomials imply those of the first companion linearizations, and the converse...
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Algebraic properties of compatible Poisson brackets
We discuss algebraic properties of a pencil generated by two compatible Poisson tensors A ( x ) and B ( x ). From the algebraic viewpoint this amounts to...
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On general principles of eigenvalue localizations via diagonal dominance
This paper suggests a unifying framework for matrix spectra localizations that originate from different generalizations of strictly diagonally...
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On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem
For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are...
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Legendre duality in combinatorial study of matrix pencils
In combinatorial studies of the Kronecker form of matrix pencils, two linear-algebraic characteristics have been featured: degrees of subdeterminants...
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Analyzing facial expressions with fuzzy quantification theory II: indefinite generalized eigenvalue problem
Machine understanding of human interactive behaviour is a challenging task. In this paper, facial expressions are used to induce emotions on a group...
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Almost sure stability condition of weakly coupled linear nonautonomous random systems
In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated....
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Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems
We show that a multiple eigenvalue has different sensitivities under perturbations in a generalized Hermitian eigenvalue problem. Our result provides...
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About the uniqueness solution of the matrix polynomial equation A(
λ )X(λ ) − Y(λ )B(λ ) = C(λ )We establish conditions for the existence of a unique solution of the matrix polynomial equation A ( λ ) X ( λ ) − Y ( λ ) B ( λ ) = C ( λ ) over an arbitrary field.
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Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation
Modern modeling approaches for circuit analysis lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of...
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On Reducible Nonmonic Matrix Polynomials with General and Nonnegative Coefficients
We consider nonmonic quadratic polynomials acting on a general or on a finite-dimensional linear space as a continuation of our work in [7,8]....
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Real Commutative Division Algebras
The category of all two-dimensional real commutative division algebras is shown to split into two full subcategories. One of them is equivalent to...
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Notes on Generalized Lemniscates
A series of analytic and geometric features of generalized lemniscates are presented from an elementary and unifying point of view. A novel interplay...
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Stability Issues in Regular and Noncritical Singular DAEs
This paper addresses equilibrium stability issues in both regular and singular differential-algebraic equations (DAEs). We present a survey of...