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1.
We investigate the structure of the multiplicative semigroup generated by the set of matrices that are unitarily equivalent to a given singular matrix A. In particular, we give necessary and sufficient conditions, in terms of the singular values of A, for such a semigroup to consist of all matrices of rank not exceeding the rank of A.  相似文献   

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We investigate the structure of the multiplicative semigroup generated by the set of matrices that are unitarily equivalent to a given singular matrix A. In particular, we give necessary and sufficient conditions, in terms of the singular values of A, for such a semigroup to consist of all matrices of rank not exceeding the rank of A.  相似文献   

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In this article the authors characterize all the 4×4 zero-nonzero patterns that are spectrally arbitrary. Several observations and conjectures are presented for the n × n case.  相似文献   

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In this article, we present new bounds for the zeros of polynomials depending on some estimates for the spectral norms and the spectral radii of the square and the cube of the Frobenius companion matrix.  相似文献   

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In this article we provide generalizations of Specht's theorem which states that two n × n matrices A and B are unitarily equivalent if and only if all traces of words in two non-commuting variables applied to the pairs (A, A*) and (B, B*) coincide. First, we obtain conditions which allow us to extend this to simultaneous similarity or unitary equivalence of families of operators, and secondly, we show that it suffices to consider a more restricted family of functions when comparing traces. Our results do not require the traces of words in (A, A*) and (B, B*) to coincide, but only to be close.  相似文献   

8.
Under a general hypothesis an expanding map T of a Riemannian manifold M is known to preserve a measure equivalent to the Liouville measure on that manifold. As a consequence of this and Birkhoff’s pointwise ergodic theorem, the orbits of almost all points on the manifold are asymptotically distributed with regard to this Liouville measure. Let T be Lipschitz of class τ for some τ in (0,1], let Ω(x) denote the forward orbit closure of x and for a positive real number δ and let E(x0, δ) denote the set of points x in M such that the distance from x0 to Ω is at least δ. Let dim A denote the Hausdorff dimension of the set A. In this paper we prove a result which implies that there is a constant C(T) > 0 such that if τ = 1 and if τ < 1. This gives a quantitative converse to the above asymptotic distribution phenomenon. The result we prove is of sufficient generality that a similar result for expanding hyperbolic rational maps of degree not less than two follows as a special case.  相似文献   

9.
For Kolmogorovs strong law of large numbers an alternative short proof is given which weakens Etemadis condition of pairwise independence. The argument uses the known – and elementary – equivalence of (Cesàro) C1- and C2-summability for one-sided bounded sequences. Also other strong laws of large numbers are established, in part via Borel summability.  相似文献   

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The extremal matrices in certain inequalities for determinants of sums are characterized. Related determinantal inequalities involving Hadamard products of positive definite matrices are presented. These inequalities are easy consequences of majorization results recently obtained by Ando and Visick.  相似文献   

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Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994  相似文献   

15.
This article presents a technique for combining two matrices, an n?×?n matrix M and an m?×?m matrix B, with known spectra to create an (n?+?m???p)?×?(n?+?m???p) matrix N whose spectrum consists of the spectrum of the matrix M and m???p eigenvalues of the matrix B. Conditions are given when the matrix N obtained in this construction is nonnegative. Finally, these observations are used to obtain several results on how to construct a realizable list of n?+?1 complex numbers (λ123,σ) from a given realizable list of n complex numbers (c 1,c 2,σ), where c 1 is the Perron eigenvalue, c 2 is a real number and σ is a list of n???2 complex numbers.  相似文献   

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Summary. We study the spectral measure of Gaussian Wigner's matrices and prove that it satisfies a large deviation principle. We show that the good rate function which governs this principle achieves its minimum value at Wigner's semicircular law, which entails the convergence of the spectral measure to the semicircular law. As a conclusion, we give some further examples of random matrices with spectral measure satisfying a large deviation principle and argue about Voiculescu's non commutative entropy. Received: 3 April 1995 / In revised form: 14 December 1996  相似文献   

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 We prove the fundamental theorems for affine immersions into hyperquadrics (including affine spaces) with arbitrary codimension, which are generalizations of those for isometric immersions into space forms. As applications, the fundamental theorems for equiaffine immersions into hyperquadrics with arbitrary codimension are obtained. (Received 10 February 2000)  相似文献   

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For a probability measure μ on a subset of , the lower and upper Lq-dimensions of order are defined by We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions and . We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension attains the smallest possible value and the upper Lq-dimension attains the largest possible value.  相似文献   

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The Flanders Theorem relates the matrices AB and BA and provides a necessary and sufficient condition for the consistency of the matrix system P = ABQ = BA In this paper, we generalize the Flanders condition for several matrices.  相似文献   

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