Results 11 to 20 of about 31,759 (192)
On the nilpotent commutator of a nilpotent matrix [PDF]
Linear and Multilinear Algebra, 2012 We study the structure of the nilpotent commutator $\nb$ of a nilpotent matrix $B$. We show that $\nb$ intersects all nilpotent orbits for conjugation if and only if $B$ is a square--zero matrix. We describe nonempty intersections of $\nb$ with nilpotent orbits in the case the $n \times n$ matrix $B$ has rank $n-2$.
Polona Oblak
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Reduction of system of partial derivatives with nilpotent matrix
Lietuvos Matematikos Rinkinys, 2000 In this paper we explain the method of squaring of the partial derivatives system with nilpotent matrix into the system with simpler matrix next to the solving function.
Donatas Jurgaitis +1 more
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Index rank-$k$ numerical range of matrices [PDF]
Journal of Mahani Mathematical Research, 2023 We introduce the $\alpha-$higher rank form of the matrix numerical range, which is a special case of the matrix polynomial version of higher rank numerical range.
Sharifeh Rezagholi, Rouholah Yasini
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Математичні Студії, 2021 We investigate a few special decompositions in arbitrary rings and matrix rings over indecomposable rings into nilpotent and idempotent elements. Moreover, we also define and study the nilpotent sum trace number of nilpotent matrices over an arbitrary ...
P.V. Danchev
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Study Some Properties of a Circulant Matrix
Tikrit Journal of Pure Science, 2023 The aim of this paper is to study the properties of idempotent, nilpotent and stability to a circulant matrix which generated by the first row, finally we showed the relation between this properties with eigenvalues of this matrix.
Akram Salim Mohammed
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Computing in Nilpotent Matrix Groups [PDF]
LMS Journal of Computation and Mathematics, 2006 AbstractWe present algorithms for testing nilpotency of matrix groups over finite fields, and for deciding irreducibility and primitivity of nilpotent matrix groups. The algorithms also construct modules and imprimitivity systems for nilpotent groups.
Detinko, A. S., Flannery, D. L.
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Chimera state in coupled map lattice of matrices
Lietuvos Matematikos Rinkinys, 2021 In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks.
Kotryna Mačernytė, Rasa Šmidtaitė
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All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two
Complexity, 2020 Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation.
Duanmei Zhou, Jiawen Ding
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Zero-sum triangles for involutory, idempotent, nilpotent and unipotent matrices
Results in Applied Mathematics, 2022 In some matrix formations, factorizations and transformations, we need special matrices with some properties and we wish that such matrices should be easily and simply generated and of integers.
Pengwei Hao, Chao Zhang, Huahan Hao
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A Matrix Model for Random Nilpotent Groups [PDF]
International Mathematics Research Notices, 2017 We study random torsion-free nilpotent groups generated by a pair of random words of length $\ell$ in the standard generating set of $U_n(\mathbb{Z})$. Specifically, we give asymptotic results about the step properties of the group when the lengths of the generating words are functions of $n$.
Delp, Kelly +2 more
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