相关论文: Linear relations and their singular chains
We consider a fixed basis of a finitely generated free chain complex as a finite topological space and we present a sufficient condition for the singular homology of this space to be isomorphic with the homology of the chain complex.
A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
This paper summarizes the core definitions and results regarding the chain differential for functions in locally convex topological vector spaces. In addition, it provides a few elementary calculus rules of practical interest, notably for…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
In this brief communication, we investigate the cospectral as well integral chain graphs for Seidel matrix, a key component to study the structural properties of equiangular lines in space. We derive a formula that allows to generate an…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Network scientists have shown that there is great value in studying pairwise interactions between components in a system. From a linear algebra point of view, this involves defining and evaluating functions of the associated adjacency…
The dynamics of multiple scalar fields on a flat FLRW spacetime can be described entirely as a relational system in terms of the matter alone. The matter dynamics is an autonomous system from which the geometrical dynamics can be inferred,…
Symmetries play a very important r\^ole in Particle Physics. In extended scalar sectors, the existence of symmetries may permit the models to comply with the experimental constraints in a natural way, and at the same time reduce the number…
We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be…
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…
In singular models, the optimal set of parameters forms an analytic set with singularities and classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular and thus…
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
The characterization of large-scale structural organization of social networks is an important interdisciplinary problem. We show, by using scaling analysis and numerical computation, that the following factors are relevant for models of…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
We consider a local action with both the real scalar field and its dual in two Euclidean dimensions. The role of singular line discontinuities is emphasized. Exotic properties of the correlation of the field with its dual, the generation of…
Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly…