The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
Linear and Multilinear Algebra, 2008 We study the set $\partition{\nb}$ of all possible Jordan canonical forms of nilpotent matrices commuting with a given nilpotent matrix $B$. We describe $\partition{\nb}$ in the special case when $B$ has only one Jordan block. In the general case, we find the maximal possible index of nilpotency in the set of all nilpotent matrices commuting with a ...
Polona Oblak
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Algorithms for computing with nilpotent matrix groups over infinite domains
Journal of Symbolic Computation, 2008 We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical algorithm to test nilpotency of matrix groups over an infinite field.
Detinko, A.S., Flannery, D.L.
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A Characterization of Affine Primal Topological Spaces Induced by Nilpotent Matrices
International Journal of Mathematics and Mathematical SciencesIn this article, we prove that an n×n matrix A is nilpotent if and only if there exists an affine primal topology τ for Rn such that the space Rn,τ is both compact and connected.
Ebner Pineda, Luis Mejías, Jorge Vielma
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Reduction of Neutrosophic Fuzzy Matrices Using Implication Operator [PDF]
Neutrosophic Sets and SystemsThis research explores the reduction of Neutrosophic Fuzzy Matrices (NFMs) and highlights their significant properties, focusing particularly on nilpotent NFMs.
K. Karuppiah +5 more
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On n-quasi- [m,C] $[m,C]$-isometric operators
Journal of Inequalities and Applications, 2019 For positive integers m and n, an operator T∈B(H) $T \in B ( H )$ is said to be an n-quasi- [m,C] $[m,C]$-isometric operator if there exists some conjugation C such that T∗n(∑j=0m(−1)j(mj)CTm−jC.Tm−j)Tn=0 . In this paper, some basic structural properties
Junli Shen
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Quick design of feasible tensor networks for constrained combinatorial optimization [PDF]
QuantumQuantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems.
Hyakka Nakada +2 more
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NILPOTENTS ZERO DIVISORS OF A MULTIDIMENSIONAL MATRIX
, 2022 In this article, the necessary conditions for nilpotency of matrices of three and higher dimensions are studied. In addition, its application to quadratic stochastic operators is presented.
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Algorithm to compute minimal matrix representation of nilpotent lie algebras
International Journal of Computer Mathematics, 2019 As it is well-known there exist matrix representations of any given finite-dimensional complex Lie algebra. More concretely, such representations can be obtained by means of an isomorphic matrix Lie algebra consisting of upper-triangular square matrices.
Ceballos, Manuel +2 more
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Index reduction for rectangular descriptor systems via feedbacks
Cogent Engineering, 2017 Index plays a fundamental role in the study of descriptor systems. For regular descriptor systems, calculation of the index can be performed by calculating the index of the nilpotent matrix obtained by means of the Weierstrass canonical form ...
Vikas Kumar Mishra +2 more
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Computational Study of Fuzzy Neutrosophic Soft Matrices in Python: Consistency and Weak Transitivity [PDF]
Neutrosophic Sets and SystemsIn this study, we introduce a novel framework for defining and analyzing two specific types of Fuzzy Neutrosophic Soft Matrices (FNSMs): consistent and weakly transitive.
M Kavitha +3 more
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