In this paper, we develop three essential ingredients of an algebraic structure theory of nite block Hankel matrices. The development centers around a transformation of block Hankel matrices, rst introduced by Fischer and Frobenius for scalar Hankel matrices. We prove three results: First, Iohvidov's fundamental notion of the characteristic of a Hankel matrix is extended to the block matrix cas...

In this paper using the Clifford algebra over R4 and its matrix representation, we construct Clifford scaling functions and Clifford wavelets. Then we compute related mask functions and filters, which arise in many applications such as quantum mechanics.

We obtain inductive and enumerative formulas for the multiplicities of weights spin module Clifford algebra a Levi subalgebra in complex semisimple Lie algebra. Our involve only matrices tableaux, our techniques combine linear algebra, theory, combinatorics. Moreover, this suggests relationship with nilpotent orbits. The case special $\mathfrak{sl}(n,{\mathbb C})$ is emphasized.

The recent introduction of generalized Appell sequences in the framework of Clifford Analysis solved an open question about a suitable construction of power-like monogenic polynomials as generalizations of the integer powers of a complex variable. The deep connection between Appell sequences and Pascal’s triangle called also attention to other number triangles and, at the same time, to the cons...

Complexified spacetime algebra is defined as the geometric (Clifford) algebra of spacetime with complex coefficients. By resorting to matrix representation by means of Dirac-Pauli gamma matrices, the paper demonstrates isomorphism between subalgebras of CSTA and SU(3). It is shown that the symmetry group of those subalgebras is indeed U(1) ⊗ SU(2) ⊗ SU(3) and that there are 4 distinct copies of...

Given a real representation of the Clifford algebra corresponding to Rp+q with metric of signature (p, q), we demonstrate the existence of two natural bilinear forms on the space of spinors. With the Clifford action of k-forms on spinors, the bilinear forms allow us to relate two spinors with elements of the exterior algebra. From manipulations of a rank four spinorial tensor introduced in [1],...