Related papers: Fast matrix representation for Clifford algebras
In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric that exists on these spaces can always be…
Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…
In computer vision, the estimation of the fundamental matrix is a basic problem that has been extensively studied. The accuracy of the estimation imposes a significant influence on subsequent tasks such as the camera trajectory…
This paper presents a thoughful review of: (a) the Clifford algebra Cl(H_{V}) of multivecfors which is naturally associated with a hyperbolic space H_{V}; (b) the study of the properties of the duality product of multivectors and…
The large systems of complex linear equations that are generated in QCD problems often have multiple right-hand sides (for multiple sources) and multiple shifts (for multiple masses). Deflated GMRES methods have previously been developed…
The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix…
Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD…
In this paper, a novel unsupervised low-rank representation model, i.e., Auto-weighted Low-Rank Representation (ALRR), is proposed to construct a more favorable similarity graph (SG) for clustering. In particular, ALRR enhances the…
Self-supervised learning on graphs has made large strides in achieving great performance in various downstream tasks. However, many state-of-the-art methods suffer from a number of impediments, which prevent them from realizing their full…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
Most algorithms for computing persistent homology do so by tracking cycles that represent homology classes. There are many choices of such cycles, and specific choices have found different uses in applications. Although it is known that…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The…
In this work we explore the structure of Clifford algebras and the representations of the algebraic spinors in quantum information theory. Initially we present an general formulation through elements of left minimal ideals in tensor…
We introduce a natural way to extend celebrated spin-cluster Monte Carlo algorithms for fast thermal lattice simulations at criticality, like Wolff, to systems in arbitrary fields, be they linear magnetic vector fields or nonlinear…
In this paper we give a thoughtful exposition of the hyperbolic Clifford algebra of multivecfors which is naturally associated with a hyperbolic space, whose elements are called vecfors. Geometrical interpretation of vecfors and…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
After a short introduction on Clifford algebras of polynomials, we give a general method of constructing a matrix representation. This process of linearization leads naturally to two fundamental structures: the generalized Clifford algebra…