In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.

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...

Systems of linear equations, with uncertainty on the parameters, play a major role in various problems in economics and finance. Fuzzy system of linear equations has been discussed in [1] using LU decomposition when the matrix A in Ax = b is a crisp matrix. Also the Adomian decomposition method and iterative methods have been studied in [2, 6] for fuzzy system of linear equations. In this paper...

1. The algorithm. Huang [1] gives an algorithm for computing the powers of a triangular matrix where the diagonal elements are unique. However, in contrast to Huang’s algorithm, the method presented here has the unique advantage of producing the result in closed form, which shows explicitly how the behavior of any element of the matrix varies with varying powers of the matrix. Also, the closed ...

We survey and compare a wide variety of techniques for estimating the condition number of a triangular matrix, and make recommendations concerning the use of the estimates in applications. Each of the methods is shown to bound the condition number; the bounds can broadly be categorised as upper bounds from matrix theory and lower bounds from heuristic or probabilistic algorithms. For each bound...

In this paper we prove that Neville elimination can be matricially described by elementary matrices. A PLU-factorization is obtained for any n×m matrix, where P is a permutation matrix, L is a lower triangular matrix (product of bidiagonal factors) and U is an upper triangular matrix. This result generalizes the Neville factorization usually applied to characterize the totally positive matrices...

The matrix equation MA = N is considered. The lgrade of a matrix A is the the largest rank of any subdiagonal block of a symmetric partition of a square matrix. When A has lgrade d, representation results are given for MA = N with M and N having lower bandwidth d. M can be chosen to be lower triangular or unitary. A second result is that if MA = N with M and N have lower bandwidths d M and d N ...

In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.

A QR–method for computing the singular values via semiseparable matrices. Abstract The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a ne...

A triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Conversely a square matrix is called upper triangular if all the entries below the main diagonal are zero. [6] For a square matrix M , M−1 is the inverse matrix where M ×M−1 = I and I denotes the n× n identity matrix. We say that the problem siz...