Linear algebra plays a key role in the theory of dynamical systems, and concepts from dynamical systems allow the study, characterization and generalization of many objects in linear algebra, such as similarity of matrices, eigenvalues, and (generalized) eigenspaces. The most basic form of this interplay can be seen as a matrix A gives rise to a continuous time dynamical system via the linear o...

In this paper,The concept of a (∈,∈ ∨q)-fuzzy ideal in an ordered Abel-Grassmann groupoid is introduced. In partcicular, left regular ordered Abel-Grassmann groupoids are characterized by using the (∈ ,∈ ∨q)-fuzzy ideals.

A relation between the Z3-graded Grassmann variables and parafermions is established. Coherent states are constructed as a direct consequence of such a relationship. We also give the analog of the Bargmann-Fock representation in terms of these Grassmann variables.

We introduce the concept of the Grassmann real form of an arbitrary matrix supergroup and of its Lie superalgebra. This new notion includes as special cases the ordinary real forms (considered and classified by Serganova) but it is more general. Indeed, the Grassmann real forms are characterized by certain Lie superal-gebra automorphisms of order four, while the ordinary real forms by those of ...

We consider an effective Majorana neutrino mass operator with the FriedbergLee symmetry; i.e., it is invariant under the transformation να → να + z (for α = e, μ, τ) with z being a space-time independent constant element of the Grassmann algebra. We show that this new flavor symmetry can be broken in such a nontrivial way that the lightest neutrino remains massless but an experimentally-favored...

We study δ-derivations – a construction simultaneously generalizing derivations and centroid. First, we compute δ-derivations of current Lie algebras and of modular Zassenhaus algebra. This enables us to provide examples of Lie algebras having 1 2 -derivations which are divisors of zero, thus answering negatively a question of Filippov. Second, we note that δ-derivations allow, in some circumst...

We derive a Newton method for computing the best rank-(r1, r2, r3) approximation of a given J × K × L tensor A. The problem is formulated as an approximation problem on a product of Grassmann manifolds. Incorporating the manifold structure into Newton’s method ensures that all iterates generated by the algorithm are points on the Grassmann manifolds. We also introduce a consistent notation for ...

A bstract Higher-form symmetries are associated with transformations that only act on extended objects, not point particles. Typically, higher-form live alongside ordinary, point-particle (0-form), and they can be jointly described in terms of a direct product symmetry group. However, when the actions 0-form become entangled, more general mathematical structure is required, related to higher ca...