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...

We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of quantum bits (i.e., a quantum computer). We report on a C++ program called “Qubiter” that implements our algorithm. Qubiter source code is publicly available.

Many of the currently popular ‘block algorithms’ are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

Many of the currently popular \block algorithms" are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by c...

Factorizations of Wiener–Hopf type are considered in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups, with a non-archimedean linear order on the dual group. A criterion for factorizability is established for 2 × 2 block triangular matrix functions with elementary functions on the main diagonal and a binomial expression in the off-diagonal...

A stable test for checking if a matrix is a nonsingular M -matrix is presented. Its computational cost is, in the worst case, O(n2) elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius less than 1.

This research aims at creating and providing a framework to describe algorithmic redistribution methods for various block cyclic decompositions. To do so properties of this data distribution scheme are formally exhibited. The examination of a number of basic dense linear algebra operations illustrates the application of those properties. This study analyzes the extent to which the general two-d...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...

A series of physically motivated operations appearing in the study composite materials are interpreted terms elementary continued fraction transforms matrix valued, rational Stieltjes functions.

1 0 2 0 1 1 (a) Suppose a2 = (1, 2, 2) , a3 = (−2, 0, 1) , a4 = (0, 4, 5) , a5 = (0, 1, 1) . Compute the ranks of A and B. Explain why B can not be obtained from A by a finite number of elementary row operations. Solution: The first 3 columns of B are independent, so its column space has dimension 3, thus rank(B)=3. The second, third and fifth column of A are independent, so its column space ha...