We prove some new equivalences of Anderson’s paving conjectures. Among these are a paving conjecture for positive matrices and for strictly upper triangular matrices.

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 consider wreath product decompositions for semigroups of triangular matrices. We exhibit an explicit wreath product decomposition for the semigroup of all n× n upper triangular matrices over a given field k, in terms of aperiodic semigroups and affine groups over k. In the case that k is finite this decomposition is optimal, in the sense that the number of group terms is equal to the group c...

X iv :m at h/ 95 12 22 4v 1 [ m at h. C O ] 1 9 D ec 1 99 5 An Explicit Formula for the Number of Solutions of X = 0 in Triangular Matrices Over a Finite Field Shalosh B. EKHAD and Doron ZEILBERGER Abstract: We prove an explicit formula for the number of n × n upper triangular matrices, over GF (q), whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov and Ann...

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...