In this paper we reduce the problem concerning the number of connected components in the intersection of two real opposite open Schubert cells in SLn(R)/B to a purely combinatorial question in the space of upper triangular matrices with F2-valued entries. The crucial step of the reduction uses the parametrization of the space of real unipotent totally positive upper triangular matrices introduc...

We study two random walks on a group of upper triangular matrices. In each case, we give upper bound on the mixing time by using a stopping time technique.

The m-th root of the diagonal of the upper triangular matrix Rm in the QR decomposition of AXB = QmRm converges and the limit is given by the moduli of the eigenvalues of X with some ordering, where A,B,X ∈ Cn×n are nonsingular. The asymptotic behavior of the strictly upper triangular part of Rm is discussed. Some computational experiments are discussed.

Among the very general scramblings introduced by A. Owen [Owe95], simple and widely used scramblings are obtained by S. Tezuka [Tez94]–[Tez95] by multiplying on the left the upper triangular generator matrices by nonsingular lower triangular (NLT) matrices whose entries are randomly chosen in the set of digits {0, 1, . . . , b − 1} identified to Fb. For these special scramblings we propose to s...

Customizable triangular factorizations of matrices find their applications in computer graphics and lossless transform coding. In this paper, we prove that any N ×N nonsingular matrix A can be factorized into 3 triangular matrices, A = PLUS, where P is a permutation matrix, L is a unit lower triangular matrix, U is an upper triangular matrix of which the diagonal entries are customizable and ca...

We completely characterize real Bott manifolds up to diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously. We also prove that any graded ring isomorphism between the cohomology rings of real Bott manifolds with Z/2 coefficients is induced by an affine diffeomorphism betwe...