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Subspaces fixed by a nilpotent matrix [PDF]
Orbita Mathematicae, 2022 The linear spaces that are fixed by a given nilpotent $n \times n$ matrix form a subvariety of the Grassmannian. We classify these varieties for small $n$.
Marvin Anas Hahn +3 more
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All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two [PDF]
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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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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Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size [PDF]
Linear Algebra and its Applications, 2022 In this paper we characterize all nilpotent orbits under the action by conjugation that intersect the nilpotent centralizer of a nilpotent matrix $B$ consisting of two Jordan blocks of the same size. We list all the possible Jordan canonical forms of the
Dusko Bogdanic +4 more
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The algebra generated by nilpotent elements in a matrix centralizer
The Electronic Journal of Linear Algebra, 2021 For an arbitrary square matrix $S$, denote by $C(S)$ the centralizer of $S$, and by $C(S)_N$ the set of all nilpotent elements in $C(S)$. In this paper, we use the Weyr canonical form to study the subalgebra of $C(S)$ generated by $C(S)_N$.
Ralph John L. de la Cruz, Eloise Misa
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Pairs of commuting nilpotent operators with one-dimensional intersection of kernels and matrices commuting with a Weyr matrix [PDF]
Linear Algebra and its Applications, 2020 I.M. Gelfand and V.A. Ponomarev (1969) proved that the problem of classifying pairs ( A , B ) of commuting nilpotent operators on a vector space contains the problem of classifying an arbitrary t-tuple of linear operators.
V. M. Bondarenko +3 more
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Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices
Nonlinear AnalysisArnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices are explored in this paper. The scalar iterative variables in the Caputo fractional standard map are replaced by iterative matrix variables.
Ugnė Orinaitė +2 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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