Related papers: Spectral square roots of the multivector

The computation of the topology of a real algebraic plane curve is greatly simplified if there are no more than one critical point in each vertical line: the general position condition. When this condition is not satisfied, then a finite…

We define a spinor Abelian variety $S_{\Delta}$ to be a complex Abelian variety whose tangent space at the origin is a space of spinors for a suitable complex Clifford algebra $\mathbb{C}_{q}(V)$. We examine intrinsic properties of such…

The concept of rotation symmetric functions from the Boolean domain is extended to the multiple-valued (MV) domain. It is shown that symmetric functions are a subset of the rotation symmetric functions. Functions exhibiting these kinds of…

By computing all cyclotomic points on some algebraic varieties, we get an independent and efficient way to find all rational $a^3b$-monotiles for the sphere, thereby completing the classification of edge-to-edge monohedral quadrilateral…

A variety of universal similarity factorization equalities over real Clifford algebras ${\cal R}_{p,q}$ are established. On the basis of these equalities, real, complex and quaternion matrix representations of elements in ${\cal R}_{p,q}$…

In this article, we develop an algebraic framework of axioms which abstracts various high-level properties of multi-qudit representations of generalized Clifford algebras. We further construct an explicit model and prove that it satisfies…

We use the combination of configuration interaction and many-body perturbation theory method (CI+MBPT) to perform ab initio calculations the low-energy spectra of Cr II with high accuracy. It is found that second-order MBPT diagrams should…

Prompted by a recent demonstration that the structure of a single quark-lepton generation may be understood via a Dirac-like linearization of the form p^2+x^2, we analyze the corresponding Clifford algebra in some detail. After classifying…

We construct invariants of relative K-theory classes of multiparameter dependent pseudodifferential operators, which recover and generalize Melrose's divisor flow and its higher odd-dimensional versions of Lesch and Pflaum. These higher…

Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…

In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work. We build our graphical calculus out of a fixed set of graphical…

Let g be a complex semi-simple Lie algebra and g be a semisimple subalgebra of g. Consider the branching problem of decomposing the simple g-representations V as a sum of simple grepresentations V. When g = g x g, it is the tensor product…

In this work, we are presenting an efficient way to compute the geometric mean of two positive definite matrices times a vector. For this purpose, we are inspecting the application of methods based on Krylov spaces to compute the square…

In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem…

We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the nth polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be…

We show that the spectral theorem -- which we understand to be a statement that every self-adjoint matrix admits a certain type of canonical form under unitary similarity -- admits analogues over other $*$-algebras distinct from the complex…

In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…

We present a combination of two algorithms that accurately calculate multiple roots of general polynomials. Algorithm I transforms the singular root-finding into a regular nonlinear least squares problem on a pejorative manifold, and…

This paper describes a geometrical method for finding the roots $r_1$, $r_2$ of a quadratic equation in one complex variable of the form $x^2+c_1 x+c_2=0$, by means of a Line $L$ and a Circumference $C$ in the complex plane, constructed…

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body…