Results 31 to 40 of about 931 (215)
Dimensions of nilpotent matrix algebras [PDF]
, 2021 This project uses graph theory and techniques from linear and abstract algebra to study the dimensions of nilpotent subalgebras of a matrix algebra. The main goal is to understand important theorems of Lie-Kolchin and Schur on these dimensions and then ...
Adwetewa-Badu, Kwabena A.
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The Unipotency of Linear Groups Generated by Matrices with No More than Five Jorden Blocks
Journal of Harbin University of Science and Technology, 2022 Aiming at the question whether the group generated by two unipotent matrices whose Jordan blocks are of order no more than five is a unipotent group, based on the fundamental definition of nilpotent matrix, we use the matrix logarithm tool to obtain some
YANG Xin-song, LI Jia-xin
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Nilpotent-independent sets and estimation in matrix algebras [PDF]
LMS Journal of Computation and Mathematics, 2015 Efficient methods for computing with matrices over finite fields often involverandomisedalgorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for such algorithms require knowledge of the proportion of relevant matrices in the ambient group or algebra.
Brian P. Corr +2 more
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Potentially nilpotent patterns and the Nilpotent-Jacobian method [PDF]
, 2012 A nonzero pattern is a matrix with entries in {0,∗}. A pattern is potentially nilpotent if there is some nilpotent real matrix with nonzero entries in precisely the entries indicated by the pattern. We develop ways to construct some potentially nilpotent
Bergsma, Hannah +5 more
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On Decompositions of Matrices over Distributive Lattices
Journal of Applied Mathematics, 2014 Let L be a distributive lattice and Mn,q (L)(Mn(L), resp.) the semigroup (semiring, resp.) of n × q (n × n, resp.) matrices over L. In this paper, we show that if there is a subdirect embedding from distributive lattice L to the direct product ∏i=1mLi ...
Yizhi Chen, Xianzhong Zhao
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On Consistent and Weak Transitive Intuitionistic Fuzzy Matrices
Fuzzy Information and Engineering, 2022 In this paper, we discuss in detail several properties of two kinds of intuitionistic fuzzy matrices which they are consistent and weak transitive. The nilpotent and transitive intuitionistic fuzzy matrices play an important role in this discussion.
E. G. Emam
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On nilpotent matrices over antirings [PDF]
, 2008 In this paper, the nilpotent matrices over commutative antirings are characterized in terms of principal permanental minors, main diagonals and permanental adjoint matrices, and a necessary and sufficient condition for a nilpotent matrix over a ...
Tan, Yijia
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On the distance from a matrix to nilpotents
Linear Algebra and its Applications, 2023 We prove that the distance from an $n\times n$ complex matrix $M$ to the set of nilpotents is at least $\frac{1}{2}\sec\fracπ{n+2}$ if there is a nonzero projection $P$ such that $PMP=M$ and $M^*M\geq P$. In the particular case where $M$ equals $P$, this verifies a conjecture by G.W. MacDonald in 1995.
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Products of nilpotent matrices [PDF]
, 1987 We show that any complex singular square matrix T is a product of two nilpotent matrices A and B with rank A = rank B = rank T except when T is a 2×2 nilpotent matrix of rank ...
Wu, Pei Yuan
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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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