Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂. In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂...

A version of Henrici's classical perturbation theorem for eigenvalues of matrices is obtained for joint spectra of commuting tuples of matrices. The approach involves Clifford algebra techniques introduced by Mcintosh and Pryde.

4 × 4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on any particular representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation ...

We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix representations of the generators of finite-dimensional Clifford algebras C(m,n). Restricting the consideration to the Clifford algebra C(4, 0), this parametrizat...

It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes are obtainable from designs that are not orthogonal also. Recently, two such classes of SSD codes have been studied: (i) Coordinate Interleaved Orthogonal De...

Using the Chern classes defined by Grothendieck, we map a K-theoretic invariant of invertible symmetric matrices defined by Giffen to the Clifford invariant.

In this paper, we establish some conjugacy criteria of Möbius groups in infinite dimension by using Clifford matrices. This extends the corresponding known results in finite dimensional setting.

Here is discussed generalization of Clifford algebras, l-dimensional Weyl–Clifford algebras T(n, l) with n generators tk satisfying equation ∑n k=1 aktk )l = ∑n k=1 (ak) . It is originated from two basic and well known constructions: representation of Clifford algebras via tensor products of Pauli matrices together with extension for l > 2 using Weyl commutation relations. Presentation of such ...

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative star products are associative and require the use of the Baker-Campbell-Hausdorff formula. Actions for pbranes in noncommutative (Clifford) spaces and noncommutative phase spaces are provided. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X, X...