Related papers: Vector Spaces of Linearizations for Multivariable …
We consider two graph models of semantic change. The first is a time-series model that relates embedding vectors from one time period to embedding vectors of previous time periods. In the second, we construct one graph for each word: nodes…
Quantum communication protocols are typically formulated in terms of abstract qudit states and operations, leaving the question of an experimental realization open. Direct translation of these protocols, say into single photons with some…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
The main purpose of this article is to show that the numerical range of a linear pencil $\lambda A + B$ is equal to $\mathbb{C}$ if and only if $0$ belongs to the convex hull of the joint numerical range of $A$ and $B$. We also prove that…
Let $\mathcal A:U\to V$ be a linear mapping between vector spaces $U$ and $V$ over a field or skew field $\mathbb F$ with symmetric, or skew-symmetric, or Hermitian forms $\mathcal B:U\times U\to\mathbb F$ and $\mathcal C:V\times…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces…
The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…
State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…
We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.
We study the structured distance to singularity for a given regular matrix pencil $A+sE$, where $(A,E)\in \mathbb S \subseteq (\mathbb C^{n,n})^2$. This includes Hermitian, skew-Hermitian, $*$-even, $*$-odd, $*$-palindromic, T-palindromic,…
Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…
Non-Hermitian matrices $H\in M_2(\mathbb{C})$ satisfying the relation $ H^{\dag}G = GH $, for invertible and singular Hermitian matrices $G$ have been studied. The matrices $H$ corresponding to invertible $G$ are known in the literature as…
We develop the theory of frames and Parseval frames for finite-dimensional vector spaces over the binary numbers. This includes characterizations which are similar to frames and Parseval frames for real or complex Hilbert spaces, and the…
The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we…
In this work, we conduct a joint analysis of both Vector Space and Language Models for IR using the mathematical framework of Quantum Theory. We shed light on how both models allocate the space of density matrices. A density matrix is shown…
We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two…
One of the main methods for computational interpretation of a text is mapping it into a vector in some embedding space. Such vectors can then be used for a variety of textual processing tasks. Recently, most embedding spaces are a product…
In this paper, we give a approximation characterization, embedding properties and the duality of matrix weighted modulation spaces.
In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties. As a consequence of this research, families such as the…