Related papers: Some thoughts about matrix coordinate transformati…
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
It is often the case in mathematical analysis that solving an open problem can be facilitated by finding a new set of coordinates which may illumniate the known difficulties. In this article, we illustrate how to derive an assortment…
An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the…
We consider a general schema involving measure spaces, contractions and linear and continuous operators. Within the framework of this schema we use our sesquilinear uniform integral and introduce some integral operators on continuous vector…
We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair…
In 2017, Bauer, Johnson, Osborne, Riehl, and Tebbe (BJORT) showed that the Abelian functor calculus provides an example of a Cartesian differential category. The definition of a Cartesian differential category is based on a differential…
We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.
In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.
Matrix Code gives imperative programming a mathematical semantics and heuristic power comparable in quality to functional and logic programming. A program in Matrix Code is developed incrementally from a specification in pre/post-condition…
Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller…
The central impediment to reducing multidimensional integrals of transition amplitudes to analytic form, or at least to a fewer number of integral dimensions, is the presence of magnitudes of coordinate vector differences (square roots of…
Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space $\Phi^\times$ in a convenient Gelfand triplet…
Many problems in Computer Vision can be reduced to either working around a known transform, or given a model for the transform computing the inverse problem of the transform itself. We will look at two ways of working with the matrix $A$…
The concept of switching has arisen in several different areas within combinatorics. The act of switching usually transforms a combinatorial object into a non-isomorphic object of the same type, in a way that some key property is preserved.…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
A higher dimensional generalization of the cross product is associated with an adequate matrix multiplication. This index-free view allows for a better understanding of the underlying algebraic structures, among which are generalizations of…
We introduce the key concepts of duality mappings and metric extensor. The fundamental identities involving the duality mappings are presented, and we disclose the logical equivalence between the so-called metric tensor and the metric…
Any associative bilinear multiplication on the set of n-by-n matrices over some field of characteristic not two, that makes the same vectors orthogonal and has the same trace as ordinary matrix multiplication, must be ordinary matrix…
In this paper we define generalizations of boson normal ordering. These are based on the number of contractions whose vertices are next to each other in the linear representation of the boson operator function. Our main motivation is to…