共查询到20条相似文献,搜索用时 15 毫秒
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A linear operator A is called reflexive if the only operators that leave invariant the invariant subspaces of A are the operators in the weak closure of the algebra of polynomials in A. In this note we completely characterize reflexive operators on finite-dimensional spaces. 相似文献
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Let (x, Xβ, V) be a linear model and let A′ = (A′1, A′2) be a p × p nonsingular matrix such that A2X = 0, Rank A2 = p − Rank X. We represent the BLUE and its covariance matrix in alternative forms under the conditions that the number of unit canonical correlations between y1 ( = A1x) and y2 ( = A2x) is zero. For the second problem, let x′ = (x′1, x′2) and let a g-inverse V− of V be written as (V−)′ = (A′1, A′2). We investigate the reations (if any) between the nonzero canonical correlations {1 1 … 1 > 0} due to y1 ( = A1x) and y2 ( = A2x), and the nonzero canonical correlations {1 λ1 … λv+r > 0} due to x1 and x2. We answer some of the questions raised by Latour et al. (1987, in Proceedings, 2nd Int. Tampere Conf. Statist. (T. Pukkila and S. Puntanen, Eds.), Univ. of Tampere, Finland) in the case of the Moore-Penrose inverse V+ = (A′1, A′2) of V. 相似文献
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Algebraically reflexive linear transformations 总被引:9,自引:0,他引:9
Don Hadwin 《Linear and Multilinear Algebra》1983,14(3):225-233
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For an n×n Boolean matrix R, let AR={n×n matrices A over a field F such that if rij=0 then aij=0}. We show that a collection AR〈1〉,…,AR〈k〉 generates all n×n matrices over F if and only if the matrix J all of whose entries are 1 can be expressed as a Boolean product of Hall matrices from the set {R〈1〉,…,R〈k〉}. We show that J can be expressed as a product of Hall matrices R〈i〉 if and only if ΣR〈i〉?R〈i〉 is primitive. 相似文献
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Let be the set of all linear transformations from to , where and are vector spaces over a field . We show that every -dimensional subspace of is algebraically -reflexive, where denotes the largest integer not exceeding , provided is less than the cardinality of .
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Let denote a field and V denote a nonzero finite-dimensional vector space over . We consider an ordered pair of linear transformations A:V→V and A*:V→V that satisfy (i)–(iii) below.
- 1. [(i)]Each of A,A* is diagonalizable on V.
- 2. [(ii)]There exists an ordering of the eigenspaces of A such thatwhere V-1=0, Vd+1=0.
- 3. [(iii)]There exists an ordering of the eigenspaces of A* such thatwhere , .
Keywords: Leonard pair; Tridiagonal pair; q-Inverting pair; Split decomposition 相似文献
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We describe necessary and sufficient conditions for orbits of linear transformations onR
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,n1, and sets arising as sums of elements from orbits, to be harmonious subsets. This is done via a generalization of the notion of Pisot-Vijayaraghavan and Salem numbers. 相似文献
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Acta Mathematica Hungarica - 相似文献
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Countable linear transformations are clean 总被引:1,自引:0,他引:1
It is shown that every linear transformation on a vector space of countable dimension is the sum of a unit and an idempotent.
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B. P. Duggal 《Mathematische Annalen》1978,237(3):277-285
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L. Makar Limanov 《代数通讯》2013,41(14):5379-5382
Let K be a field and let σ(t) be an automorphism of k(t) of infinite order. In his paper [1] Gerard Cauchon asked whether the transformation which is naturally defined on kU∞ by σ has infinitely many infinite orbits. This is indeed so. 相似文献
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William D. L. Appling 《Annali di Matematica Pura ed Applicata》1985,140(1):147-154
Summary Suppose U is a set,F is a field of subsets of U, pAB is the set of all real-valued bounded finitely additive functions defined onF, and for each in pAB, A()={: in pAB, absolutely continuous with respect to }. SupposeM is a linear subspace of pAB such that
. A generalisation of a previously discussed collection of linear transformations (see J. London Math. Soc., vol. 44 (1969), pp. 385–396) is treated by letting CM denote the set to which T belongs iff T is a linear transformation from M into pAB such that for some K inR and all in M and V inF,
. Certain theorems of the aforementioned reference are generalized, as well as one of Trans. Amer. Math. Soc., vol. 199, (1974), pp. 131–140. The principal result of the present paper is the following generalisation of a reversibility characterisation in the first mentioned reference: Theorem: If T is in CM, then (, T()): in M A(T()) is the only reversible subset T0 if T such that: i) the domain M0 of T0 is a linear subspace of M and
, and ii) the range of T0 is the range of T. 相似文献