In this paper, we prove that the world of near-vector spaces allows us to work with non-linear problems and yet, gives access to most of the tools linear algebra has to offer. We establish some fundamental results for near-vector spaces toward extend...
May 10, 2007 · A rank 3 tensor inputs three generalized vectors (i.e. either a vector or their dual vector), and spits out a scalar. One can also think of it as inputting 2 generalized vectors (or a rank 2 tensor), …
Every tensor is associated with a linear map that produces a scalar. For instance, a vector can be identified with a map that takes in another vector (in the presence of an inner product) and produces …
Feb 11, 2024 · A tensor extends the notion of a matrix analogous to how a vector extends the notion of a scalar and a matrix extends the notion of a vector. A tensor can have any number of dimensions, …
Jun 18, 2017 · Tensor Product Properties Definition: A tensor product of vector spaces is a vector space structure on the Cartesian product that satisfies This means a tensor product is a freely generated …
This work describes the R package GET that implements global envelopes for a general set of $d$-dimensional vectors $T$ in various applications. A $100(1-α)$% global envelope is a band bounded by two vectors such that the probability that $T$ falls...
We prove new non-existence results for vectorial monomial Dillon type bent functions mapping the field of order $2^{2m}$ to the field of order $2^{m/3}$. When $m$ is odd and $m>3$ we show that there are no such functions. When $m$ is even we derive a...
The $\dbar$-dressing scheme based on local nonlinear vector $\dbar$-problem is developed. It is applicable to multidimensional nonlinear equations for vector fields, and, after Hamiltonian reduction, to heavenly equation. Hamiltonian reduction is d...
We calculate the group of dualization operations for triple vector bundles, showing that it has order 96 and not 72 as given in Mackenzie's original treatment. The group is a nonsplit extension of S4 by the Klein group. Dualization operations are i...
In this paper, we propose Vo-Ve, a novel voice-vector embedding that captures speaker identity. Unlike conventional speaker embeddings, Vo-Ve is explainable, as it contains the probabilities of explicit voice attribute classes. Through extensive anal...
This study performs an ablation analysis of Vector Quantized Generative Adversarial Networks (VQGANs), concentrating on image-to-image synthesis utilizing a single NVIDIA A100 GPU. The current work explores the nuanced effects of varying critical par...
This paper presents an indirect method for measuring the switch terms of a vector network analyzer (VNA) using at least three reciprocal devices, which do not need to be characterized beforehand. This method is particularly suitable for VNAs that use...
The aim of this paper is to establish some new results on the absolute continuity and the convergence in total variation for a sequence of d-dimensional vectors whose components belong to a finite sum of Wiener chaoses. First we show that the probabi...
Multi-vector visual retrievers (e.g., ColPali-style late interaction models) deliver strong accuracy, but scale poorly because each page yields thousands of vectors, making indexing and search increasingly expensive. We present Visual RAG Toolkit, a...
Download free Milwaukee Bucks vector logo and icons in PNG, SVG, AI, EPS, CDR formats.
The Milwaukee Bucks logo in vector format (svg) and transparent PNG. Ready to download.
Knowledge editing aims to efficiently correct factual errors in language models. Widely used locate-then-edit methods update an MLP layer by adjusting its weights to change the mapping between the layer's input vector (key) and output vector (value),...
We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of $sl_{2}$ (Theorem 3). The formula is derived from a...
Dec 26, 2025 · Let (X, n) (X, n) be normed space and B B a basis (by basis I mean a set of vector such that every vector in X can be expressed in an essentially unique way as a finite linear combination of …
We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus $g\geq 2$. This is a classical result from the 1960s, obtained using geometric invariant theory. We outline a modern approach that combines the recent ma...