LetX = LσU be the Gelfand-Naimark decomposition of X ∈ GLn(C), where L is unit lower triangular, σ is a permutation matrix, and U is upper triangular. Call u(X) := diagU the u-component of X. We show that in a Zariski dense open subset of the ω-orbit of certain Bruhat decomposition, lim m→∞ |u(X)| = diag (|λω(1)|, · · · , |λω(n)|). The other situations where lim m→∞ |u(X)| converge to different...

In this paper we show that the group inverse of a real singular Toeplitz matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes “Gohberg–Semencul formula” in the literature. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A09; 65F20

The lgrade of a n × n matrix A is the largest rank of any subdiagonal block of a symmetric partition of A. A number of algebraic results on lgrade are given. When A has lgrade d, it can be be approximately decomposed as A = U + V , where U is an upper triangular matrix and V has rank d. If A satisfies GA = N with G and N have lower bandwidths dG and dN , then the decomposition is exact: A = U +...

If r = 12 and (uij) is the matrix of the U operator in the above basis, then the numbers uij satisfy a recurrence formula: there is a p × p matrix M such that uij = ∑p r,s=1Mrsui−r,j−s. Furthermore, M is skew-upper-triangular and constant on off diagonals; and the coefficients uij satisfy uij = jiuji. The case p = 2 is extensively studied in [BC05]. Here the recurrence relation is simple enough...

We present a parallelization of Parlett s algorithm for computing arbitrary functions of upper triangular matrices The parallel algorithm preserves the numerical stability properties of the serial algorithm and is suitable for implementation on coarse grain parallel computers The algorithm ob tains a speedup of for matrices of size greater than as our analysis and actual implementation on a pro...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...

Assume that a1j 6= 0 for j = 2 . . . n. Then the (1, 1) element of A∗A is equal to a11+a12+. . .+a1n. The (1, 1) element of AA∗ is equal to a11. Since A is normal, a 2 11 + a 2 12 + . . . + a 2 1n = a 2 11 and, therefore, a1j = 0 for j = 2 . . . n. Now assume that a2j 6= 0 for j = 3 . . . n. Using the above proven fact that a12 = 0 we can compare the (2,2) entries of A∗A and AA∗ to show that al...

Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless communication. The complexity of the different systems models challenge different researches to get a good complexity to performance balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovàsz (LLL) algorithm bring more resources to investigate and can contribute to the complexity reduction ...

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see R. Bacher. Determinants of matrices related to the Pascal triangle. J. Théor. Nombres Bordeaux, 14:19–41, 2002). This article presents a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Toeplitz matrix, and a unipotent upper triang...

In this paper, the UDUT decomposition of the generalized inertia matrix o f an n-link serial manipulator is presented in symbolic form, where U and D, respectively, are the upper triangular and diagonal matrices. To render the decomposition, the elementary upper triangular matrices, associated to a modified Gaussian elimination, are introduced, whereas each element of the inertia matrix is writ...