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...

In a previous paper, we described a computer program called Qubiter which decomposes an arbitrary unitary matrix U into elementary operations of the type used in quantum computation. In this paper, we describe one way of reducing the number of elementary operations in such decompositions.

this paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. first, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. this new algorithm ca...

In [1] and [2] a new family of companion forms associated to a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in [3] where the scalar case was considered. In this paper, extending this “permuted factors” approach, we present a broader family of companion like linearizations, using products of up...

For the cause of Representation Theory it is important to understand the elementary ideas that go into the idea of decomposition of a linear transformation into transformations on smaller dimensional vector-spaces. It is desirable that a given linear transformation on an ndimensional vector-space is writable as a ”direct sum” of n linear transformations on one-dimensional subspaces of the origi...

Using the method of the block matrix construction and generalized elementary transformation given in the paper, readers can easily prove the inequalities of rank of matrix on skew field. Mathematics Subject Classification: 05A19; 15A15

This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. This new algorithm ca...

An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition SVD of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible ...

In this note I give a proof of the existence of a Smith normal form for matrices with integer entries. The existence of a good basis for a lattice with a finite index sublattice is a consequence of the Smith normal form. I conclude with an easy application to toric varieties. Theorem 1. Let A be a matrix with integer entries. Then there exist integer-values invertible matrices C and B such that...