共查询到20条相似文献,搜索用时 15 毫秒
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Peter Berkics 《Linear and Multilinear Algebra》2017,65(10):2114-2123
AbstractIn this note, I gather different definitions of the parallel sum of matrices, including the ones which work in infinite dimension as well. I describe the algebraic and analytic properties of this matrix operation, some interesting inequalities and its relation with other operator means. 相似文献
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Kezheng Zuo 《Linear algebra and its applications》2010,433(2):476-918
Groß and Trenkler 1 pointed out that if a difference of idempotent matrices P and Q is nonsingular, then so is their sum, and Koliha et al2 expressed explicitly a condition, which combined with the nonsingularity of P+Q ensures the nonsingularity of P-Q. In the present paper, these results are strengthened by showing that the nonsingularity of P-Q is in fact equivalent to the nonsingularity of any combination aP+bQ-cPQ (where a≠0,b≠0,a+b=c), and the nonsingularity of P+Q is equivalent to the nonsingularity of any combination aP+bQ-cPQ (where a≠0,b≠0,a+b≠c). 相似文献
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L. N. Vaserstein 《Linear and Multilinear Algebra》1987,21(3):261-270
A theorem of Lagrange says that every natural number is the sum of 4 squares. M. Newman proved that every integral n by n matrix is the sum of 8 (-1)n squares when n is at least 2. He asked to generalize this to the rings of integers of algebraic number fields. We show that an n by n matrix over a a commutative R with 1 is the sum of squares if and only if its trace reduced modulo 2Ris a square in the ring R/2R. It this is the case (and n is at least 2), then the matrix is the sum of 6 squares (5 squares would do when n is even). Moreover, we obtain a similar result for an arbitrary ring R with 1. Answering another question of M. Newman, we show that every integral n by n matrix is the sum of ten k-th powers for all sufficiently large n. (depending on k). 相似文献
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It is shown that the generalized inverses characterize the parallel sum. The almost positive definite (a.p.d.) matrices introduced by Duffin and Morley [2] are of two types, whose intersection is the class of quasi-positive-definite matrices (Mitra and Puri [7]). The a.p.d. matrices of any one type form a “saturated” subclass of pairwise parallel summable a.p.d. matrices. 相似文献
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Stanislav Kupin 《Comptes Rendus Mathematique》2003,336(7):611-614
We use sum rules of a special form to study spectral properties of Jacobi matrices. As a consequence of the main theorem, we obtain a discrete counterpart of a result by Molchanov, Novitskii and Vainberg (Comm. Math. Phys. 216 (2001) 195–213). To cite this article: S. Kupin, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
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B. T. Rumov 《Mathematical Notes》1992,52(1):716-720
A theorem is proved to the effect that if there exists a BIB-schema with parameters (pm–1,k, k–1), where k¦(pm–1), p is prime, and m is a natural number, then there exists a BIB-schema (pmn–1),k, k–1). A consequence is the existnece of a cyclic BIB-schema (pmn–1, pm–1, pm–2) (pm–1 is prime) that specifies each ordered pair of difference elements at any distance = 1, 2, ..., pm–2 (cyclically) precisely once. Recursive theorems on the existence of difference matrices and (v, k, k)-difference families in the group Zv of residue classes mod v are proved, along with a theorem on difference families in an additive abelian group.Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 114–119, July, 1992. 相似文献
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On difference matrices,resolvable transversal designs and generalized Hadamard matrices 总被引:1,自引:0,他引:1
Dieter Jungnickel 《Mathematische Zeitschrift》1979,167(1):49-60
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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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V. M. Petrichkovich 《Journal of Mathematical Sciences》1999,96(2):3022-3025
We describe all the factorizations A=BC (up to associates) of a matrix A over a commutative principal ideal domain parallel to the factorization DA= of its canonical diagonal form DA ( and are diagonal matrices), that is, the factorizations such that the matrices B and C are equivalent to the matrices and respectively.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 96–100. 相似文献
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Vladimir Nikiforov 《Linear algebra and its applications》2011,435(10):2394-2401
In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. The trace norm is just one of the Ky Fan k-norms, given by the sum of the k largest singular values, which are studied more generally in the present paper. Several relations to chromatic number, spectral radius, spread, and to other fundamental parameters are outlined. Some results are extended to more general matrices. 相似文献
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Yutaka Hiramine 《Designs, Codes and Cryptography》2014,72(3):627-635
A \(k\times u\lambda \) matrix \(M=[d_{ij}]\) with entries from a group \(U\) of order \(u\) is called a \((u,k,\lambda )\) -difference matrix over \(U\) if the list of quotients \(d_{i\ell }{d_{j\ell }}^{-1}, 1 \le \ell \le u\lambda ,\) contains each element of \(U\) exactly \(\lambda \) times for all \(i\ne j.\) Jungnickel has shown that \(k \le u\lambda \) and it is conjectured that the equality holds only if \(U\) is a \(p\) -group for a prime \(p.\) On the other hand, Winterhof has shown that some known results on the non-existence of \((u,u\lambda ,\lambda )\) -difference matrices are extended to \((u,u\lambda -1,\lambda )\) -difference matrices. This fact suggests us that there is a close connection between these two cases. In this article we show that any \((u,u\lambda -1,\lambda )\) -difference matrix over an abelian \(p\) -group can be extended to a \((u,u\lambda ,\lambda )\) -difference matrix. 相似文献
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G. A. Bekishev 《Mathematical Notes》1990,47(3):236-239
Translated from Matematicheskie Zametki, Vol. 47, No. 3, pp. 11–16, March, 1990. 相似文献
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We completely describe the determinants of the sum of orbits of two real skew symmetric matrices, under similarity action of orthogonal group and the special orthogonal group respectively. We also study the Pfaffian case and the complex case. 相似文献
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Marco Buratti 《组合设计杂志》1998,6(3):165-182
We present a new recursive construction for difference matrices whose application allows us to improve some results by D. Jungnickel. For instance, we prove that for any Abelian p-group G of type (n1, n2, …, nt) there exists a (G, pe, 1) difference matrix with e = Also, we prove that for any group G there exists a (G, p, 1) difference matrix where p is the smallest prime dividing |G|. Difference matrices are then used for constructing, recursively, relative difference families. We revisit some constructions by M. J. Colbourn, C. J. Colbourn, D. Jungnickel, K. T. Phelps, and R. M. Wilson. Combining them we get, in particular, the existence of a multiplier (G, k, λ)-DF for any Abelian group G of nonsquare-free order, whenever there exists a (p, k, λ)-DF for each prime p dividing |G|. Then we focus our attention on a recent construction by M. Jimbo. We improve this construction and prove, as a corollary, the existence of a (G, k, λ)-DF for any group G under the same conditions as above. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 165–182, 1998 相似文献