Representations of SO(5) q are constructed explicitly on the Chevalley basis for all q, generic and root of unity. Matrix elements of the generators are obtained for all representations depending on three variable indices, the maximal number being 4. A prescription for contraction is given such that a complete Hopf algebra is immediately obtained for the non-semisimple contracted case. For q a ...

For a q × q matrix x = (xi,j) we let J(x) = (x −1 i,j ) be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x) = (xi,j) −1 denote the matrix inverse, and we define K = I ◦J to be the birational map obtained from the composition of these two involutions. We consider the iteratesK = K◦· · ·◦K and determine degree complexity of K, which is the exponential rate of deg...

A procedure for designing exact reconstruction lter banks for tree-structured sub-band coders. where p(n) = jx(n)j 2 =kxk 2. Note that d = exp H(x) where H(x), deened in Equation 55 above, is the entropy of the sequence x. Beylkin in 1] observed earlier that computing the periodic discrete wavelet transform of all N circulant shifts of an N-point periodic signal requires computing only N log 2 ...

the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...

Enumerating the isomorphism classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory (see [R. Feng, J.H. Kwak, J. Kim, J. Lee, Isomorphism classes of concrete graph coverings, SIAM J. Discrete Math. 11 (1998) 265–272; R. Feng, J.H. Kwak, Typical circulant double coverings of a circulant graph, Discrete Math. 277 (2004) 73–85; R. F...

The Circulant Travelling Salesman Problem (CTSP) is the problem of nding a minimum weight Hamiltonian cycle in a weighted graph with circulant distance matrix. The computational complexity of this problem is not known. In fact, even the complexity of deciding Hamiltonicity of the underlying graph is unkown. This paper presents necessary and suucient conditions for the existence of a Hamilto-nia...

In this work we present some matrix operators named circulant operators and their action on square matrices. This study on square matrices provides new insights into the structure of the space of square matrices. Moreover it can be useful in various fields as in agents networking on Grid or large-scale distributed self-organizing grid systems. Keywords— Pascal matrices, Binomial Recursion, Circ...