We study the neutrino mixing matrix (MNS matrix) in seesaw model. Assuming large mass hierarchy for heavy right-handed Majorana mass, we show that MNS matrix is determined by a unitary matrix which transforms neutrino yukawa term into a triangular form. Large mixing may occur even if yukawa matrix for charged lepton and that for neutrino is simultaneously diagonalized by biunitary transformatio...

In this article, a new numerical method based on triangular functions for solving  nonlinear stochastic differential equations is presented. For this, the stochastic operational matrix of triangular functions for It^{o} integral are determined. Computation of presented method is very simple and attractive. In addition, convergence analysis and numerical examples that illustrate accuracy and eff...

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...

This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

We prove a lower bound of 52n 2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.

Nakajima conjectured in [N] that the transition matrix between certain PBW-basis constructed in [LXZ] and the affine canonical basis is upper triangular with the diagonal entries equal to one and the upper diagonal entries in vZ[v]. In this paper, we show that the transition matrix between the PBW-basis in [LXZ] and the canonical basis is upper triangular with the diagonal entries equal to one ...

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

We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen’s triangular tridiagonalization. It factors a dense symmetric matrix A as the product A = PLTLP where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding fac...

We deal with matrix transformations preserving the starshape of sequences. The main result gives the necessary and sufficient conditions for a lower triangular matrix A to preserve the starshape of sequences. Also, we discuss the nature of the mappings of starshaped sequences by some classical matrices. 2000 Mathematics Subject Classification. 40C05, 40D05, 40G05.