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OF SKEWSYMMETRIC MATRICES ∗
"... Abstract. Every real skewsymmetric matrix B admits Choleskylike factorizations B = R T JR, where ..."
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Abstract. Every real skewsymmetric matrix B admits Choleskylike factorizations B = R T JR, where
Commutators of SkewSymmetric Matrices
, 2004
"... In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in M n [R] and so(n) This paper is concerned with the following question. Let g b ..."
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In this paper we develop a theory for analysing the size of a Lie bracket or commutator in a matrix Lie algebra. Complete details are given for the Lie algebra so(n) of skew symmetric matrices. 1 Norms and commutators in M n [R] and so(n) This paper is concerned with the following question. Let g
Shifted SkewSymmetric Systems
"... We describe the MRS 3 solver, a Minimal Residual method based on the Lanczos algorithm that solves problems from the important class of linear systems with a shifted skewsymmetric coefficient matrix using short vector recurrences. The MRS 3 solver is theoretically compared with other Krylov solvers ..."
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We describe the MRS 3 solver, a Minimal Residual method based on the Lanczos algorithm that solves problems from the important class of linear systems with a shifted skewsymmetric coefficient matrix using short vector recurrences. The MRS 3 solver is theoretically compared with other Krylov
On The Geometry Of Varieties Of Invertible Symmetric And SkewSymmetric Matrices
, 1997
"... this paper we first determine the toplogy of the real varieties Sym(n; R) and Sk(n; R). More precisely, we show that Sym(n; R) has the homotopy type of a Grassmannian by constructing a homotopy equivalence and compute the Betti numbers of Sk(n; R) by fibering this variety over the sphere and using t ..."
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this paper we first determine the toplogy of the real varieties Sym(n; R) and Sk(n; R). More precisely, we show that Sym(n; R) has the homotopy type of a Grassmannian by constructing a homotopy equivalence and compute the Betti numbers of Sk(n; R) by fibering this variety over the sphere and using the associated Leray spectral sequence. The SerrePoincar'e polynomial (weight polynomial) of a complex algebraic variety X is defined to be
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong
Choleskylike Factorizations of SkewSymmetric Matrices
 Electr. Trans. Num. Anal
, 2000
"... Every real skewsymmetric matrix B admits Choleskylike factorizations B = R T JR, where J = # 0 I I 0 # . This paper presents a backwardstable O(n 3 ) process for computing such a decomposition, in which R is a permuted triangular matrix. Decompositions of this type are a key ingredi ..."
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Cited by 23 (5 self)
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Every real skewsymmetric matrix B admits Choleskylike factorizations B = R T JR, where J = # 0 I I 0 # . This paper presents a backwardstable O(n 3 ) process for computing such a decomposition, in which R is a permuted triangular matrix. Decompositions of this type are a key
On The Preconditioning Of Matrices With A Dominant SkewSymmetric Component
, 2000
"... . The rates of convergence of iterative methods with standard preconditioning techniques such as ILUT [9] usually degrade when the skewsymmetric component S of the matrix is relatively large. In this paper, we address the issue of preconditioning matrices with such large skewsymmetric component. Th ..."
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Cited by 2 (1 self)
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. The rates of convergence of iterative methods with standard preconditioning techniques such as ILUT [9] usually degrade when the skewsymmetric component S of the matrix is relatively large. In this paper, we address the issue of preconditioning matrices with such large skewsymmetric component
On the holonomy of connections with skewsymmetric torsion
"... Abstract. We investigate the holonomy group of a linear metric connection with skewsymmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any nondegenerated 2form or any spinor. Suitable integral formulas allow us to pro ..."
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Cited by 34 (6 self)
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Abstract. We investigate the holonomy group of a linear metric connection with skewsymmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any nondegenerated 2form or any spinor. Suitable integral formulas allow us
On the Singularity of Multivariate SkewSymmetric Models
, 2009
"... In recent years, the skewnormal models introduced by Azzalini (1985)—and their multivariate generalizations from Azzalini and Dalla Valle (1996)—have enjoyed an amazing success, although an important literature has reported that they exhibit, in the vicinity of symmetry, singular Fisher information ..."
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Cited by 11 (8 self)
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? The present paper provides an answer to this question. In very general (possibly multivariate) skewsymmetric models, we characterize, for each possible value of the rank of Fisher information matrices, the class of symmetric kernels achieving the corresponding rank. Our results show that, for strictly
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