Matrix transpose in parallel systems typically involves costly all-to-all communications. In this paper, we provide a comparative characterization of various efficient algorithms for transposing small and large matrices using the popular symmetric multiprocessors (SMP) architecture, which carries a relatively low communication cost due to its large aggregate bandwidth and lowlatency inter-proce...

in this paper, we show that a matrix a in mn(c) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. and also show that if allconeigenvalues of conjugate-normal matrix a be real, then it is symmetric.

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.

Inspired by recent work in the theory of central projections onto hyper-surfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert– Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symme...

We study the asymmetric respectively symmetric conflict matrix of a multi-clause-set F , where the entry at position (i, j) is the number of literals, which appear positively in clause Ci of F and negatively in clause Cj (at the same time), respectively the number of clashes (at all) between Ci and Cj . A central problem is the determination of the symmetric/asymmetric conflict number of a (sym...

The goal of this paper is to prove the Central Limit Theorem for linear statistics of the eigenvalues of real symmetric band random matrices with independent entries. First, we define a real symmetric band random matrix. Let {bn} be a sequence of integers satisfying 0 ≤ bn ≤ n/2 such that bn → ∞ as n → ∞. Define dn(j, k) := min{|k − j|, n− |k − j|}, (1.1) In := {(j, k) : dn(j, k) ≤ bn, j, k = 1...

Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert–Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetr...

The covariance matrix of a pattern is composed by its second order central moments. For a rotationally symmetric shape, its covariance matrix is a scalar identity matrix. In this work, we apply this property to restore the skewed shape of rotational symmetry. The relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived. By computing ...