Related papers: Angles between subspaces
The article reviews some of the (fairly scattered) information available in the mathematical literature on the subject of angles in complex vector spaces. The following angles and their relations are considered: Euclidean, complex, and…
We apply a new notion of angle between projections to deduce criteria for uniform convergence results of the alternating projections method under several different settings: averaged projections, cyclic products, quasi-periodic products and…
In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant…
The objective of the current paper is essentially twofold. Firstly, to make clear the difference between two notions of rolling a Riemannian manifold over another, using a language accessible to a wider audience, in particular to readers…
Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set…
In the paper we give a complete classification of schemes of abstract perspectives between two tetrahedrons such that intersecting edges corespond under this perspective to intersecting edges.
We study gravitational algebras on spacetimes with two extremal surfaces. In the example of a long wormhole with two asymptotic AdS boundaries and two compact extremal surfaces, we discuss the assignment of gravitational algebras to various…
With the help of link diagrams with decorated crossings, I explain computations in emergent algebras, introduced in arXiv:0907.1520, as the kind of computations done in the front end visual system.
Objects dual to graded algebras are subproduct systems of linear spaces, a purely algebraic counterpart of a notion introduced recently in the context of noncommutative dynamics (Shalit and Solel, Bhat and Mukherjee). A complete…
Some examples and basic properties of ultrametric spaces are briefly discussed.
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships…
The space of embedded submanifolds plays an important role in applications such as computational anatomy and shape analysis. We can define two different classes on Riemannian metrics on this space: so-called outer metrics are metrics that…
We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
In the 3-dimensional Berwald-Moor space are bingles and tringles constructed, as additive characteristic objects associated to couples and triples of unit vectors - practically lengths and areas on the unit sphere. In analogy with the…
This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some…
Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of norm equivalence. Angularly equivalent norms share certain…
Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner…
Grassmannians are of fundamental importance in projective geometry, algebraic geometry, and representation theory. A vast literature has grown up utilizing using many different languages of higher mathematics, such as multilinear and tensor…