共查询到20条相似文献,搜索用时 15 毫秒
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Maximal semigroups dominated by a 0–1 matrix of a certain type are determined. The 0–1 matrices that dominate maximal bounded
and maximal commuting semigroups are given. Also semigroup modules over maximal semigroups dominated by a 0–1 matrix are discussed. 相似文献
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Pace P. Nielsen 《Proceedings of the American Mathematical Society》2007,135(9):2689-2697
Consider the ring of all column finite matrices over a ring . We prove that each such matrix is conjugate to a row and column finite matrix if and only if is right Noetherian and is countable. We then demonstrate that one can perform this conjugation on countably many matrices simultaneously. Some applications and limitations are given.
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Pierre Antoine Grillet 《Semigroup Forum》1972,4(1):327-334
Any semigroup can be quite explicitly rebuilt from its quotient by any congruence contained in ℋ and certain groups and mappings.
This fact underlies most of the classical and recent structure theorems in semigroup theory, and yields new ones, e.g. concerning
finite commutative semigroups. 相似文献
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Hailegebriel Gessesse Alexey I. Popov Heydar Radjavi Eugeniu Spinu Adi Tcaciuc Vladimir G. Troitsky 《Positivity》2010,14(3):383-394
A semigroup \({\mathfrak{S}}\) of non-negative n × n matrices is indecomposable if for every pair i, j ≤ n there exists \({S\in\mathfrak{S}}\) such that (S) ij ≠ 0. We show that if there is a pair k, l such that \({\{(S)_{kl} : S\in\mathfrak{S}\}}\) is bounded then, after a simultaneous diagonal similarity, all the entries are in [0, 1]. We also provide quantitative versions of this result, as well as extensions to infinite-dimensional cases. 相似文献
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《Linear algebra and its applications》2006,412(2-3):490-525
Characterizations are given for automorphisms of semigroups of nonnegative matrices including doubly stochastic matrices, row (column) stochastic matrices, positive matrices, and nonnegative monomial matrices. The proofs utilize the structure of the automorphisms of the symmetric group (realized as the group of permutation matrices) and alternating group. Furthermore, for each of the above (semi)groups of matrices, a larger (semi)group of matrices is obtained by relaxing the nonnegativity assumption. Characterizations are also obtained for the automorphisms on the larger (semi)groups and their subgroups (subsemigroups) as well. 相似文献
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Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient conditions for A in the semigroup Gn(C) to be primitive are given. We also show that Gc(Jn) is a subsemigroup of Gn(C). 相似文献
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In this paper we study the semigroups of matrices over a commutative semiring. We prove that a semigroup of matrices over a tropical semiring satisfies a combinatorial property called weak permutation property. We consider an application of this result to the Burnside problem for groups. 相似文献
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A. Skryago 《Semigroup Forum》1977,15(1):95-101
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On the structure of semigroups of idempotent matrices 总被引:1,自引:0,他引:1
Karin Cvetko-Vah 《Linear algebra and its applications》2007,426(1):204-213
We prove that any pure regular band of matrices admits a simultaneous LU decomposition in the standard form. In case that such a band forms a double band called a skew lattice, we obtain the standard form without the assumption of purity. 相似文献
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Lassi Paunonen 《Journal of Evolution Equations》2014,14(4-5):885-911
In this paper, we study the stability properties of strongly continuous semigroups generated by block operator matrices. We consider triangular and full operator matrices whose diagonal operator blocks generate polynomially stable semigroups. As our main results, we present conditions under which also the semigroup generated by the operator matrix is polynomially stable. The theoretical results are used to derive conditions for the polynomial stability of a system consisting of a two-dimensional and a one-dimensional damped wave equation. 相似文献
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If a nonzero linear functional has finite, countable, or bounded range when restricted to an irreducible semigroup
of complex matrices, it is shown that
itself has the same property. Similar results are proven under the hypothesis that a nontrivial ideal of
is finite, countable, or bounded. 相似文献
16.
Walter S. Sizer 《Linear algebra and its applications》1977,16(2):177-187
We define a closure operation on semigroups of matrices over a skew field, and show that a semigroup of matrices can be (upper) triangularized if and only if its closure can be. We then give necessary and sufficient conditions for a closed semigroup to be triangularizable. 相似文献
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Fernando Guevara Vasquez Benjamin Z. Webb 《Numerical Linear Algebra with Applications》2015,22(1):145-174
An isospectral matrix reduction is a procedure that reduces the size of a matrix while maintaining its eigenvalues up to a known set. As to not violate the fundamental theorem of algebra, the reduced matrices have rational functions as entries. Because isospectral reductions can preserve the spectrum of a matrix, they are fundamentally different from say the restriction of a matrix to an invariant subspace. We show that the notion of pseudospectrum can be extended to a wide class of matrices with rational function entries and that the pseudospectrum of such matrices shrinks with isospectral reductions. Hence, the eigenvalues of a reduced matrix are more robust to entry‐wise perturbations than the eigenvalues of the original matrix. Moreover, the isospectral reductions considered here are more general than those considered elsewhere. We also introduce the notion of an inverse pseudospectrum (or pseudoresonances), which indicates how stable the poles of a rational function valued matrix are to entry‐wise perturbations. Illustrations of these concepts are given for mass‐spring networks. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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