共查询到20条相似文献,搜索用时 46 毫秒
1.
We study matrices over general rings which are sums of nilpotent matrices. We show that over commutative rings all matrices with nilpotent trace are sums of three nilpotent matrices. We characterize 2-by-2 matrices with integer entries which are sums of two nilpotents via the solvability of a quadratic Diophantine equation. Some exemples in the case of matrices over noncommutative rings are given. 相似文献
2.
幂等右侧Quantale上的幂零矩阵 总被引:2,自引:0,他引:2
讨论幂等右侧Quantale上的幂零矩阵的若干性质,给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件,得到了幂零矩阵的幂零指数的刻画定理。 相似文献
3.
Hiroshi Hashimoto 《Discrete Applied Mathematics》1984,8(1):51-61
Boolean matrices are widely used in many fields, and the theory of boolean matrices is related to the algebra of relations, switching theory, and graph theory. First some basic properties of nilpotent matrices are shown in the paper. A nilpotent boolean matrix plays an important role in the theory of boolean matrices. The purpose is to present those properties of boolean matrices which are related to finding the transitive reduction of a nilpotent matrix, or an acyclic graph. 相似文献
4.
Let S be an antinegative commutative semiring without zero divisors and M_n(S)be the semiring of all n×n matrices over S.For a linear operator L on M_n(S),we say that L strongly preserves nilpotent matrices in M_n(S)if for any A∈M_n(S),A is nilpotent if and only if L(A)is nilpotent.In this paper,the linear operators that strongly preserve nilpotent matrices over S are characterized. 相似文献
5.
In this note we describe explicitly those linear spaces of nilpotent matrices, which are stable under conjugation by diagonal matrices. As an application, we deduce a generalized version of a result of Valcher and Fornasini on pairs of nonnegative nilpotent matrices. 相似文献
6.
In this paper, we introduce a new class of upper triangular nilpotent matrices, etermine the eigenvalues of the Hermitian part of rotating the type of nilpotent matrices and relate the numerical range of that typical type of matrices to the orbit of a point mass under a central force. 相似文献
7.
A. R. Sourour 《Linear and Multilinear Algebra》2013,61(1-4):303-308
We show that, with the exception of 2 × 2 nonzero nilpotent matrices, every singular square matrix over an arbitrary field is a product of two nilpotent matrices. 相似文献
8.
9.
10.
David Dol?an 《Linear algebra and its applications》2011,435(7):1649-1656
We study diameters and girths of noncommuting graphs of semirings. For a noncommutative semiring that is either multiplicatively or additively cancellative, we find the diameter and the girth of its noncommuting graph and prove that it is Hamiltonian. Moreover, we find diameters and girths of noncommuting graphs of all nilpotent matrices over a semiring, all invertible matrices over a semiring, all noninvertible matrices over a semiring, and the full matrix semiring. In nearly all cases we prove that diameters are less than or equal to 2 and girths are less than or equal to 3, except in the case of 2×2 nilpotent matrices. 相似文献
11.
12.
13.
Zejun Huang 《Linear algebra and its applications》2011,434(4):880-883
A sign pattern is said to be nilpotent of index k if all real matrices in its qualitative class are nilpotent and their maximum nilpotent index equals k. In this paper, we characterize sign patterns that are nilpotent of a given index k. The maximum number of nonzero entries in such sign patterns of a given order is determined as well as the sign patterns with this maximum number of nonzero entries. 相似文献
14.
David Dol?an 《Linear algebra and its applications》2011,435(7):1657-1665
We calculate diameters and girths of commuting graphs of the set of all nilpotent matrices over a semiring, the group of all invertible matrices over a semiring, and the full matrix semiring. 相似文献
16.
解决了幂等和幂零阵的伴随阵的反问题,把Sherman-Morrison公式[1]推广到求伴随阵的情形,并给出了一类伴随还原阵的简单求法. 相似文献
17.
Polona Oblak 《Linear algebra and its applications》2008,428(7):1476-1491
In this paper we completely characterize all possible pairs of Jordan canonical forms for mutually annihilating nilpotent pairs, i.e. pairs (A,B) of nilpotent matrices such that AB=BA=0. 相似文献
18.
19.
David Dol?an 《Linear algebra and its applications》2009,430(1):271-2258
In this paper, we characterize invertible matrices over an arbitrary commutative antiring S with 1 and find the structure of GLn(S). We find the number of nilpotent matrices over an entire commutative finite antiring. We prove that every nilpotent n×n matrix over an entire antiring can be written as a sum of ⌈log2n⌉ square-zero matrices and also find the necessary number of square-zero summands for an arbitrary trace-zero matrix to be expressible as their sum. 相似文献
20.
J. D. Botha 《Linear and Multilinear Algebra》1994,38(1):145-150
We give necessary and sufficient conditions for a singular matrix over an arbitrary field to be factorized into a product of two nilpotent matrices with prescribed ranks. 相似文献