Results 11 to 20 of about 1,700,750 (206)
Transitive reduction of a nilpotent boolean matrix
Discrete Applied Mathematics, 1984 Given an acyclic digraph, a problem which frequently arises in applications consists in removing the maximum number of arcs without affecting reachability. This removal corresponds to a so-called transitive reduction of the adjacency matrix of the given digraph.
Hashimoto, Hiroshi
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Some nilpotent and locally nilpotent matrix groups
Journal of Pure and Applied Algebra, 1989 The task of the paper under review is a detailed discussion of nilpotent and locally nilpotent matrix groups over ``special'' division rings. The notion of a ``special'' division ring is introduced by the author and denotes a division ring D with the following property: For every finite subset X of D and every finite subset Y of the subring R of D ...
Wehrfritz, B.A.F.
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A Maximality Criterion for Nilpotent Commutative Matrix Algebras
Canadian Mathematical Bulletin, 1974 Let A be a commutative algebra contained in Mn(F), F a field. Then A is nilpotent if there exists v such that Av=(0), and is said to have nilpotency class k (denoted Cl(A)=k) if Ak=(0), but Ak-1≠(0). A well known result asserts that matrix algebras are nilpotent if and only if every element is nilpotent.
Handelman, D., Selick, P.
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ENUMERATION OF IDEALS OF SOME NILPOTENT MATRIX RINGS
Journal of Algebra and Its Applications, 2012 Using the method of integral representation of combinatorial sums we enumerate ideals of certain nilpotent matrix rings.
KUZUCUOĞLU, FERİDE +2 more
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The algebra generated by nilpotent elements in a matrix centralizer [PDF]
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 $C(S)_N$. We determine conditions on $S$ such that $C(S)_N$ is a subalgebra of $C(S)$.
Ralph John De la Cruz, Eloise Misa
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A Note on Decomposing a Square Matrix as Sum of Two Square Nilpotent Matrices over an Arbitrary Field [PDF]
The Scientific World Journal, 2013 Let be an arbitrary field and a square matrix over . Then is sum of two square nilpotent matrices over if and only if, for every algebraic extension of and arbitrary nonzero , there exist idempotent matrices and over such that .
Xiaofei Song +2 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 ApplicationsIn 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 nilpotent matrices that commute with $B$ by characterizing the corresponding partitions.
Bogdanić, Duško +4 more
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Enumerating finite class-2-nilpotent groups on 2 generators [PDF]
, 2009 We compute the numbers g(n,2,2) of nilpotent groups of order n, of class atmost 2 generated by at most 2 generators, by giving an explicit formula for theDirichlet generating function \sum_{n=1}^\infty g(n,2,2)n^{-s}
Voll, Christopher, Christopher Voll
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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.
A. S. Detinko, Dane L. Flannery
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Applications of Lie methods to computations with polycyclic groups [PDF]
, 2008 In this thesis we demonstrate the algorithmic usefulness of the so-called Mal'cev correspondence for computations with infinite polycyclic groups.
Assmann, Björn
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